THE  MECHANICS 
OF  ELECTRICITY 


.  '  :".'. 


GIFT  OF 
Mrs*   F.J.B.    Gordeiro 


PUBLICATIONS  BY  THE  AUTHOR 

SPON  &  CHAMBERLAIN,  NEW  YORK 


BAROMETRICAL  DETERMINATION  OF  HEIGHTS. 

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THE  ATMOSPHERE. 

A  Manual  of  Meteorology  $1.50 

THE  GYROSCOPE. 

Theory  and  Applications  $1.50 

THE  MECHANICS  OF  ELECTRICITY. 

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THE  MECHANICS  OF 
ELECTRICITY 


BY 

F.  J.  B.  CORDEIRO 

AUTHOR  OF 

"THE  GYROSCOPE,"   "THE  ATMOSPHERE,"  "BAROMETRICAL 
HEIGHTS,"  ETC. 


NEW  YORK: 
SPON  &  CHAMBERLAIN,  123  LIBERTY  STREET 

LONDON: 

E.  &  F.  N.  SPON,  LIMITED,  57  HAYMARKET,  S.W. 

1915 


£,!> 


COPYRIGHT,  1915, 

BY 

c  J.  B.  CORDEIRO 


PINKHAM  PRESS 
BOSTON,  U.S.A 


PREFACE 


When  asked  what  electricity  is,  physicists  a  few  years 
ago  would  reply,  "We  do  not  know,"  and  the  inquirer  was 
made  to  feel  that  he  had  asked  a  foolish  question.  To 
Maxwell,  electricity  itself  seems  to  have  been  rather 
an  abstraction,  and  he  occupied  himself  chiefly  with 
its  effects,  or  the  strains  it  produces  in  dielectrics. 
To  the  ultra-Maxwellians  who  declare  that  "there  is 
no  such  thing  as  electricity,"  it  is  a  disembodied  spirit, 
not  necessarily  connected  with  matter  except  in  so  far 
as  this  is  necessary  to  render  its  effects  observable. 

The  general  consensus  of  opinion  at  present  is  that 
electricity  is  something.  Lodge  writes,  "Electricity  may 
possibly  be  a  form  of  matter — it  is  not  a  form  of  energy. 
We  have  nowhere  asserted  that  electricity  and  the  ether 
are  identical.  If  they  are,  we  are  bound  to  admit  that 
the  ether,  though  fluid  in  the  sense  of  enabling  masses  to 
move  freely  through  it,  has  a  certain  amount  of  rigidity 
for  enormously  rapid  and  minute  oscillatory  disturbances. 
Is  the  ether  electricity  then?  I  do  not  say  so,  neither  do 
I  think  that  in  that  coarse  statement  lies  the  truth;  but 
that  they  are  connected  there  can  be  no  doubt." 

Clausius  surmised  that  electricity  might  be  the  ether, 
and  if  we  may  judge  from  certain  passages  the  surmise 
amounted  to  a  belief.  This  belief  was,  of  course,  not 
based  upon  any  direct  proof,  for  that  is  hardly  possible, 
but  was  rather  of  the  nature  of  an  intuition.  He  seems 
to  have  been  alone  in  this  opinion. 


5  7 1 ; j 


vi  PREFACE 

The  object  of  this  book  is  to  show  that  electricity  and 
the  ether  are  identical.  The  ether  is  electricity  and 
electricity  is  the  ether.  It  has  been  sought,  through  the 
cumulative  and  corroborative  evidence  of  the  phenomena 
to  raise  a  presumption  that  amounts  almost  to  a  certainty. 


THE   ETHER 


Electricity  not  many  years  ago  was  classed  as  a  force 
of  nature,  of  which  there  were  a  number  of  different 
kinds,  separate  and  distinct.  These  different  natural 
forces  were  given  categorically  as  mechanical,  electrical, 
gravitational,  magnetic,  vital,  cohesional,  chemical,  etc., 
and,  as  the  conception  of  force  is  intimately  connected 
with  that  of  energy  or  work,  there  were  as  many  different 
kinds  of  energy.  Heat  was  considered  still  another  form 
of  energy,  and  light  still  another. 

Eventually  it  was  recognized  that  some,  at  least,  of 
these  forms  of  energy  were  mutually  convertible,  and  the 
doctrine  of  the  conservation  of  energy  led  to  the  view  that 
energy  was  a  single  entity,  though  capable  of  manifesta- 
tion under  a  number  of  different  forms.  The  next  step 
was  that  force  under  all  circumstances  was  a  single  entity — 
essentially  the  same  under  whatsoever  guise  it  might 
present  itself.  It  was  recognized  that  in  the  universe 
only  two  cardinal  entities  were  observable,  viz.,  matter 
and  force.  The  universe  was  seen  to  consist  actually  of 
matter  alone,  albeit  of  many  different  kinds,  and  this 
matter,  or  materies,  was  found  to  be  indestructible  and 
non-reproducible.  The  doctrine  of  the  conservation  of 
matter  was  founded  by  Lavoisier. 

Now  this  matter  was  found  to  be  capable  of  changing 
its  position  in  space,  both  absolutely  and  relatively  to 
other  matter:  in  other  words  it  was  capable  of  motion. 
And  to  effect  this  motion  it  was  found  that  force  had  to 
be  applied  directly  to  the  matter.  Whatever  influenced 
the  motion  of  matter,  whether  by  originating  the  motion, 

1 


ELECTRICAL 


&r:  changing  a,cpf  coexisting  motion,  or  stopping  the  motion* 
was  force.  It  was  found  that  all  matter  offered  a  resistance 
to  having  its  condition  of  motion,  or  no  motion,  changed, 
and  this  resistance  to  such  a  change  was  called  inertia. 
It  was  further  found  that  although  matter  at  rest  was 
dead,  yet  while  in  motion  it  carried  a  store  of  energy  which 
could  be  abstracted  from  it  and  transferred  elsewhere, 
while  from  the  principle  of  the  conservation  of  energy, 
since  it  possessed  only  a  certain  definite  store,  its  energy 
was  necessarily  lessened  by  the  exact  amount  which  had 
been  abstracted. 

The  universe,  therefore,  consists  of  matter,  either  dead 
or  living,  i.e.,  either  at  rest  or  in  motion.  And  we  may 
define  force  as  that  which  influences  the  motion  of  matter, 
and  thereby  stores  up  energy  in  it,  or  abstracts  energy 
from  it.  Force  implies  change  of  motion  and  energy,  and 
vice  versa.  We  must  further  recognize  that  a  force  cannot 
impart  motion,  and  consequently  store  up  energy,  unless 
it  acts  directly  on  matter.  It  cannot  act  at  a  distance,  as 
was  until  recently  supposed.  A  body  cannot  exert  a 
gravitational  force  upon  another  body  through  empty 
space,  nor  an  electrical  action,  nor  a  magnetic  action,  nor 
an  action  of  any  kind.  But  it  can  and  does  exert  such 
actions  through  intervening,  closely  connecting  matter  — 
in  other  words  through  a  medium.  It  will  be  further  seen 
that  any  action  of  a  force  upon  matter  must  be  of  the 
nature  of  a  push,  and  that  a  force  cannot  drag  or  pull 
matter  into  motion.  The  action  must  be  directly  towards 
the  body  acted  upon,  not  away  from  it.  To  sum  up  the 
universe  consists  only  of  matter,  plus  force  or  motion  or 
energy,  as  we  please.  There  are  only  two  factors  —  matter 
and  the  three  cognate  entities,  force,  motion  or  energy, 
which  are  only  different  expressions  for  a  single  under- 
lying entity.* 

*  Ostwald  has  proposed,  instead  of  recognizing  only  matter  and 
force,  to  recognize  only  matter  and  energy.  Such  a  contention 
is  purely  metaphysical  and  of  no  value. 


MECHANICS  3 

It  follows  that  in  studying  the  action  of  bodies  on  each 
other  at  a  distance,  we  must,  if  we  wish  to  understand  them, 
examine  particularly  the  medium  connecting  them.  For 
we  have  seen  that  there  must  be  throughout  a  direct 
material  connection  between  such  bodies:  otherwise  no 
action  can  take  place.  When  we  hear  a  sound  from  a 
distant  point  we  know  that  the  action  is  transferred  through 
the  air.  There  is  a  continuous  material  chain  between  us 
and  the  sounding  body.  If  there  were  a  single  break,  or 
interruption  of  matter,  at  any  point,  by  even  an  infinitesi- 
mal thickness,  we  should  be  unable  to  hear  the  sound. 
There  was  a  time  when  the  necessity  of  a  continuous 
material  connection  for  sound  was  not  recognized.  It 
was  supposed  to  act  at  a  distance — through  nothing. 
And  only  very  recently  has  the  necessity  of  a  continuous 
material  connection,  or  medium,  been  recognized  for  all 
actions — electrical,  magnetic,  gravitational,  etc.  The 
medium,  by,  and  through  which,  all  the  more  important 
actions  at  a  distance  are  carried  on,  is  the  Ether,  and  we 
shall  now  examine  this  chief  medium  of  the  universe. 

The  ether,  both  in  volume  and  mass,  constitutes  over- 
whelmingly the  greater  part  of  the  material  universe. 
The  amount  of  ordinary  gross  matter,  or  matter  which  is 
not  ether,  is  almost  infinitesimal  in  proportion,  and  yet  it 
is  only  within  a  comparatively  few  years  that  man  has 
become  conscious  of  its  existence.  So  far  as  we  at  present 
know,  it  has  only  three  properties.  It  may  have  many 
more,  but  these,  at  least,  are  the  only  ones  we  have  been 
able  to  recognize.  It  is  a  fluid,  i.e.,  all  bodies  move  freely 
through  it,  and  it  moves  freely  through  the  interstices  of 
all  bodies.  It  moves  freely  through  intermolecular  spaces, 
and  even  through  intramolecular  spaces.  It  penetrates 
through  molecules,  but  not  through  atoms:  so  that  it 
occupies  all  space  with  the  exception  of  that  occupied  by 
the  atoms  of  gross  matter.  It  is  always  under  a  strain, 
or  tension,  exerting  a  very  heavy  pressure.  It  is  capable 


4  ELECTRICAL 

of  compression  and  expansion,  thereby  varying  its  density. 
It  is  therefore  elastic.  It  possesses  enertia,  and  is  there- 
fore matter.  It  is  capable  of  propagating  a  disturbance, 
thereby  exhibiting  in  a  combined  form  its  two  properties 
of  elasticity  and  inertia,  since  these  two  qualities  are 
necessary  and  sufficient  for  the  transference  of  a  dis- 
turbance. It  should  be  stated  that  it  has  been  held,  and 
is  even  now  held  in  some  quarters,  that  the  ether  is  devoid 
of  elasticity,  i.e.,  incompressible.  This  was  to  explain 
the  seeming  existence  of  transverse  vibrations  in  this 
medium.  But  such  an  explanation  is  self -contradictory. 
If  it  were  incompressible  it  could  propagate  no  waves  at 
all.  Further  a  fluid  cannot  execute  transverse  vibrations, 
that  being  a  property  of  solids.  To  meet  this,  it  was 
stated  that  it  was  not  a  fluid,  but  a  kind  of  solid.  Thus 
its  two  manifest  properties  of  fluidity  and  elasticity  were 
denied  to  explain  a  supposed  property  of  transmitting 
transverse  vibrations — a  property  which  it  has  never 
possessed  and  cannot  possess.  Even  then  the  object  is 
defeated,  for,  by  removing  its  elasticity,  all  possibility  of 
wave  propagation  is  cut  off.  We  shall  see  later  on  that  the 
ether  is  capable  of  simulating  transverse  vibrations,  but 
no  true  transverse  vibrations  are  possible. 

We  have  said  that  the  ether  is  matter,  but  it  differs 
most  extraordinarily  from  ordinary  gross  matter.  While 
ordinary  matter  is  built  up  of  discrete  units — molecules 
and  atoms — the  ether  seems  to  be  a  continuum.  It  is 
matter,  but  of  a  very  simple  kind;  or  matter  reduced  to 
its  simplest  terms.  Its  fluidity  and  continuity  are  not 
so  much  properties  as  negations  of  properties,  since  the 
discrete  and  solid  and  liquid  properties  of  ordinary  matter 
are  highly  differentiated  conditions  from  a  simple,  ele- 
mentary condition.  Its  elasticity  may  possibly  be  a  con- 
comitant and  necessary  adjunct  of  its  inertia,  so  that 
these  two  properties  may  possibly  represent  a  single 
fundamental  and  underlying  property.  Hence  the  ether 


MECHANICS  5 

may  be  matter  in  its  simplest  form,  from  which  all  gross 
matter  has  been  differentiated,  and  the  single  fundamental 
property  of  all  matter  may  be  simply  inertia. 

The  ether  has  no  internal  friction,  or  viscosity,  or  any 
friction  at  all,  a  property  which  all  gases  possess;  but  since 
this  property  in  gross  matter  is  due  to  its  molecular 
structure,  it  is  naturally  wanting  in  a  continuum.  A  fluid 
without  any  friction  or  viscosity  is  called  a  perfect  fluid, 
and  hence  the  ether  is  the  only  perfect  fluid.  Differing  so 
extraordinarily  from  gross  matter,  we  may  expect  that 
its  elasticity  and  inertia  will  differ  extraordinarily  from 
the  corresponding  properties  in  gross  matter.  And  we 
find  that  such  is  the  case.  It  is  impossible  to  measure 
these  quantities  directly,  but  we  may  judge  indirectly 
from  their  effects  what  the  amount  must  be.  The  ratio 
of  the  elasticity  to  the  density,  or  inertia,  has  been  de- 
termined with  some  degree  of  exactness.  In  any  medium, 
longitudinal  waves,  which  are  waves  of  a  peculiar  type, 
are  propagated  with  a  velocity  which  is  equal  to  the  square 

root  of  the  elasticity  divided  by  the  density, or  V  =  +l  —  (1). 

Now  it  is  possible  for  a  fluid  medium  to  transmit  dis- 
turbances of  two  totally  different  types,  viz.,  waves  with 
longitudinal  vibrations,  and  what  are  known  as  electro- 
magnetic waves,  with  which  we  shall  later  on  become  famil- 

E 
iar.     The  ratio  ~  has  been  determined  by  measuring  the 

velocity  of  electro-magnetic  disturbances  in  the  ether,  on 
the  assumption  that  Equation  (1)  holds  for  such  dis- 
turbances. Since  the  intimate  mechanism  of  such  waves 
was  not  then  known,  such  an  assumption  was  hardly 
warranted.  There  was  no  doubt  that  Equation  (1)  held 
for  longitudinal  waves,  but  it  was  not  at  all  certain  that 
electro-magnetic  waves  might  not  be  propagated  with  a 
totally  different  velocity.  However,  it  turns  out,  as  we 
shall  see,  that  all  disturbances  are  propagated  with  prac- 


6  ELECTRICAL 

tically  the  same  velocity  in  an  isotropic  fluid  medium. 
The  square  root  of  our  ratio  is  something  like  3  X 1010  centi- 
meters per  second,  or  about  186,000  miles  per  second.  This 
shows  that  the  pressure,  or  elasticity,  of  the  ether  must 
be  extraordinarily  high.  What  the  actual  values  of  the 
two  quantities  are,  we  do  not  yet  certainly  know,  though 
we  may  make  a  guess.  We  may  attempt  a  rough 
estimate  from  two  phenomena — magnetism  and  cohesion. 
We  shall  see  that  magnetic  lines  of  force  are  linear  vortices 
in  the  ether,  in  the  interior  of  which  the  pressure  is  con- 
siderably less  than  that  of  the  general  ether,  and  that 
magnetic  "attraction"  between  two  bodies  is  due  to  this 
general  pressure  striving  to  close  the  partial  (or  complete) 
vacuum.  If  we  could  obtain  an  absolute  vacuum,  then 
the  force  of  such  an  attraction  would  be  a  measure  of  the 
general,  or  normal,  ether  pressure,  and  by  Equation  (1) 
we  could  obtain  the  density.  Now  the  greatest  magnetic 
force  which  it  has  as  yet  been  possible  to  obtain,  is  some- 
thing like  2000  pounds  to  the  square  inch,  or  roughly  a  ton 
to  the  square  inch.  The  question  arises,  "How  much  of 
an  absolute  ether  vacuum  does  this  represent?"  We  shall 
see  that  under  the  enormous  and  sudden  voltages  em- 
ployed in  generating  electro-magnetic  waves,  it  is  quite 
possible  that  actual  ether  vacua  are  attained  in  the  axes 
of  the  magnetic  lines  of  force,  but  in  the  very  moderate  and 
steady  voltages  employed  in  the  lifting  experiment  de- 
scribed above,  it  is  improbable  that  any  great  rarefaction 
can  be  obtained.  Still  we  may  say  that  it  is  probably 
1^0  °f  a  perfect  vacuum,  or  something  of  that  order. 
When  we  say  "of  that  order,"  we  mean  that  it  is  probably 
something  like  that,  although  it  may  vary  by  JQ  either  way. 
If  we  could  be  tolerably  sure  of  estimating  its  value  within 
a  tenth,  that  would  be  sufficient.  Assuming  that  a  force 
of  2000  pounds  to  the  square  inch  corresponds  to  about 
of  a  perfect  vacuum,  we  should  have,  as  the  general 


MECHANICS  7 

pressure  of  the  ether,  about  2,000,000  pounds  to  the  square 
inch,  which  is  1.4  X 1011  dynes  per  square  centimeter.  This 
would  make  its  density,  by  Equation  (1),  something  like 
10~10  that  of  water.  This  is  probably  somewhere  near 
the  truth  showing  that  the  ether  has  a  most  extraordinary 
tenuity,  while  exerting  an  enormous  pressure.  The  pres- 
sure is  intelligible  when  we  reflect  that  it  belongs  to  a 
single  continuous  mass,  bounded  only  by  the  confines  of 
the  universe.  This  great  resistance  of  the  ether  to  com- 
pression has  sometimes  been  referred  to  as  its  rigidity, 
which  is  manifestly  a  misuse  of  terms.  The  ether,  being 
a  perfect  fluid,  has,  of  course,  no  rigidity.  A  fluid  under 
a  pressure  of  a  thousand  pounds  is  no  whit  more  rigid  than 
when  under  a  pressure  of  one  pound. 

We  may  consider  then  the  density  of  all  gross  matter, 
or  the  density  of  all  atoms,  as  roughly  something  like 
1010  times  that  of  the  ether.  Taking  the  view  that  the 
ether  is  the  ground  stuff  out  of  which  all  forms  of  gross 
matter  have  been  elaborated,  it  is  evident  that  it  must  have 
been  by  some  process  of  condensation,  though  under  what 
conditions  such  an  enormous  condensation  was  effected, 
it  seems  difficult  to  imagine.  If  this  view  is  correct,  it  is 
quite  intelligible  how  the  numerous  infinite  properties 
ascribed  by  the  schoolmen  to  atoms,  may  be  derived,  viz., 
infinite  hardness,  unbreakableness,  uncrushableness,  in- 
finite elasticity,  infinite  smoothness,  and  what  not. 

Assuming  that  the  phenomenon  of  cohesion  is  due  to  the 
close  co-aptation  of  the  surfaces  of  atoms,  which  are  thus 
pressed  together  by  the  total  pressure  of  the  ether,  we 
find,  for  steel,  that  the  cohesion  or  tenacity  is  something 
like  100  tons  to  the  square  inch.  For  unspun  silk,  which 
is  the  strongest  substance  we  are  acquainted  with,  it  is 
nearly  three  times  as  much.  This  changes  our  estimate 
but  little,  so  that  we  might  consider  the  pressure  of  the 
ether  as  somewhere  between  1010  and  1011  dynes  per 
square  centimeter,  and  its  density  as  somewhere  between 


8  ELECTRICAL 

10-10  and  10-11  that  of  water,  or  of  atoms  in  general. 
These  estimates  are  to  be  considered  rather  as  a  minimum, 
and  the  actual  values  may  be  somewhat  more. 

Lodge,  starting  from  Lord  Kelvin's  vortex  theory  of  atoms, 
argues  that  as  they  occupy  only  a  portion  of  the  space  bounding 
a  body,  and  as  they  are  the  only  material  parts  of  the  body,  the 
density  of  the  ether,  which  is  a  continuum,  must  be  much  greater 
than  that  of  gross  matter.  He  considers  that  the  vortex  rings 
which  constitute  the  atoms  have  the  identical  density  of  the 
ether,  but,  as  they  are  few  and  far  between,  the  net  density,  as 
compared  with  the  ether,  is  almost  infinitesimal.  According  to 
his  reckoning  the  pressure  is  1033  dynes  per  square  centimeter,  which 
corresponds  to  an  amount  of  energy  equal  to  1033  ergs  in  every 
cubic  centimeter.  The  density  is  1012.  Taking  only  a  cubic 
millimeter  of  space,  the  ether  energy  in  this  small  space  he  states  to 
be  "Equal  to  the  energy  of  a  million  horse-power  station  working 
continuously  for  forty  million  years."  And  there  is,  in  a  cubic 
millimeter,  "A  mass  equivalent  to  what,  if  it  were  matter,  we  should 
call  1000  tons."  This  estimate  is  too  low,  for  the  density  of  a 
vortex  ring  is  not  that  of  the  general  ether,  but  much  less. 

It  is  hardly  necessary  to  say  that  the  vortex  theory  of  atoms 
is  not  a  very  safe  hypothesis  to  start  from,  even  though  Lodge 
argues  that  "It  is  so  good  that  it  deserves  to  be  true."  It  is  doubt- 
ful if  Lord  Kelvin  himself  ever  considered  it  more  than  a  "curious 
speculation."  We  shall  show  later  on  that  gross  matter  must  be 
very  much  more  dense  than  the  ether. 

In  our  further  study  of  the  ether,  it  is  evident  that  we 
can  only  become  aware  of  the  existence  of  this  medium 
through  its  motion.  Dead  ether,  or  ether  at  rest,  can  in 
no  way  affect  our  senses,  either  directly  or  indirectly;  so 
that  we  are  now  forced  to  inquire  into  what  kinds  of  motion 
are  possible  in  such  a  material  as  we  know  the  ether  to  be. 
Generally,  we  may  say  there  is  only  one  kind  of  motion — 
a  motion  of  certain  portions  relatively  to  others,  or  a 
streaming  or  flowing  of  certain  portions  past  others,  con- 
stituting ether  currents.  Whether  the  ether  ever  streams 
over  great  distances,  as  seems  indicated  by  the  immense 
spiral  nebulas,  where  gross  matter  may  be  in  the  process 
of  condensation  and  worlds  are  being  formed,  lies  beyond 


MECHANICS  9 

our  present  scope.  We  shall  confine  ourselves  to  cases 
where  it  flows  from  a  point  of  higher  pressure  to  a  point 
of  lower  pressure  over  finite  distances,  as  in  conductors: 
and  over  infinitesimal  distances  in  the  free  ether.  In  the 
free  ether  there  may  be  a  flow  over  very  short  distances 
from  a  point  of  higher  pressure  to  one  of  lower  pressure, 
consisting  of  a  surging  backward  and  forward  between  a 
condition  of  compression  to  one  of  rarefaction.  Such 
short  alternating  ether  currents  are  the  essence  of  all 
longitudinal  waves,  and  we  know  that  such  waves  must 
exist  in  a  fluid  like  the  ether,  possessing  both  elasticity  and 
inertia.  Further  linear  vortices  may  exist  in  such  a 
medium,  consisting  of  closed  current  sheets  surrounding 
an  axis  of  lesser  density  than  the  general  ether.  And  such 
linear  vortices  will  persist  indefinitely,  since  there  is  no 
friction  in  the  ether  between  its  different  parts.  The 
excess  pressure  of  the  external  ether  is  supported  by  the 
centrifugal  force  of  the  rapidly  rotating  current  sheet. 
Or,  designating  the  outward  centrifugal  force  of  the  cur- 
rent sheet  per  unit  of  surface  by/,  and  the  interior  pressure 
by  Pi,  while  the  external,  or  normal  pressure  isP,/  =P — Pi. 
These  linear  vortices  will  always  form  closed  curves,  for 
while  it  is  conceivable  that  the  two  ends  of  a  vortex  fila- 
ment might  be  closed  by  two  atoms,  or  by  two  continuous 
surfaces  of  atoms — the  only  bodies  impermeable  to  the 
ether — we  do  not  know  certainly  of  any  such  instances. 

There  are  further  two  ways  in  which  a  disturbance  may 
be  propagated  in  such  a  medium,  viz.,  by  longitudinal 
waves  of  the  well-known  form,  and  by  the  translation 
through  the  ether  of  such  vortex  rings  as  we  have  just 
considered,  constituting  what  are  known  as  electro- 
magnetic waves. 

The  above  varieties  of  motion  are  the  only  ones  possible 
in  such  a  medium,  and  we  may  tabulate  them  as  follows : 

1.  Simple  currents,  where  the  ether  moves  in  an  effort 
to  relieve  an  increased  pressure,  driven,  as  we  say,  by  an 


10  ELECTRICAL 

electro-motive  force:  or  where  the  ether  continues  in 
motion  from  its  own  inertia,  without  any  driving  force  and 
meeting  with  no  resistance,  such  as  is  the  case  with  the 
current  sheets  in  our  vortex  rings. 

2.  Longitudinal  waves,   which  are  propagated  by  a 
series  of  regularly  alternating  currents  in  the  direction  of 
the  wave. 

3.  Electro-magnetic  waves,  which  consist  of  a  spread- 
ing out  of  vortex  rings  through  space. 


LONGITUDINAL  WAVES 
IN  THE  ETHER 


We  shall  first  consider  longitudinal  waves  in  the  ether, 
which,  since  their  perfect  analogy  is  found  in  air  waves, 
have  happily  been  completely  studied.  Since  a  fluid 

medium,  whether  a  gas  or  the 
ether,  possesses  inertia,  any 
thrust  against  it  will  be  resisted 
just  as  much  as  if  it  were  a 
solid.  The  reaction  will  be 
p.  x  i  equal  and  opposite  to  the  action. 

Since  it  is  elastic,  the  medium 

will  be  compressed  between  these  two  forces  acting  in 
opposite  directions;  and  since  it  is  free  to  move,  it  will 
move  also  in  the  direction  of  the  force.  The  action  of  the 
thrust  is  therefore  double.  It  sets  the  medium  in  motion 
and  at  the  same  time  compresses  it,  in  each  process  doing 
work  and  thereby  storing  up  energy  in  the  medium.  The 
first  kind  of  energy  is  called  kinetic  energy  and  the  energy 
of  compression  is  called  potential  energy.  This  latter 
form  of  energy  is  also,  in  the  last  analysis,  kinetic,  or  due 
to  motion,  though  this  motion  is  concealed  and  not  as 
manifestly  evident  to  the  senses.  Thus  the  energy  of  a 
compressed  gas,  or  its  potential  energy,  is  due  to  the  motion 
of  its  molecules,  for  we  have  seen  that  energy  and  motion 
are  inseparable.  Likewise  the  pressure  of  the  ether  indi- 
cates a  huge  store  of  potential  enefgy,  which  must  be  due 
to  motion  of  some  sort,  though  of  the  nature  of  this 
motion,  we  are  as  yet  in  complete  ignorance.  It  may 

11 


12  ELECTRICAL 

possibly  be  due  to  extremely  minute  vortices  pressed 
together,  their  current  sheets  moving  with  the  standard 
velocity  of  the  medium,  in  which  case  the  ether  would  be 
a  discrete  structure.  Such  a  structure  would  enable  it 
to  have  very  great  energy  (pressure)  with  little  mass,  for 
energy  consists  of  two  factors — mass  and  motion.  Beyond 
the  normal  pressure,  at  some  point  which  we  might  call 
the  critical  pressure,  it  might  be  possible  to  break  down 
these  vortices  and  condense  them  into  non-vortical  gross 
matter.  But  every  indication  seems  to  point  against  a 
discrete  structure,  and  rather  to  a  continuum,  in  which 
case  the  energy  may  possibly  be  due  to  a  general  pulsation 
throughout  its  mass.  We  shall  consider  the  ether  a  con- 
tinuum, avoiding  all  speculation  as  to  its  internal  motion. 
Let  us  suppose  our  medium  divided  off  into  laminae 
of  equal  thickness,  1,2,  3,  4,  as  represented  in  Fig.  1.  Let 
us  further  suppose  that  lamina  1  has  been  thrust  by  a  force 
to  the  right,  thereby  having  imparted  to  it  the  two  forms 
of  energy  described  above.  It  is  evident  that  these  two 
forms  of  energy  will  be  limited  at  the  first  short  interval 
of  time  to  the  immediate  vicinity  of  the  thrust,  but  as 
time  goes  on  the  changed  portions  of  the  medium  will 
shift  their  positions  and  the  disturbance  will  travel  along 
as  a  wave.  The  lower  portion  of  Fig.  1  indicates  the 
instantaneous  position  and  condition  of  the  laminae  after 
a  certain  interval  of  time  has  elapsed.  The  disturbance 
has  extended  to  the  outer  boundary  of  4,  but  not  beyond. 
Let  Vi,  vz,  vs,  Vt,  be  the  velocities  of  the  laminae  at  any 
instant,  and  Ci,  c2,  cs,  c*,  the  distances  through  which 
they  have  been  compressed.  Now  every  lamina  opposes 
to  compression  the  original  pressure  it  possessed,  which  is 
the  normal  pressure  of  the  medium,  and  which  we  will 
designate  by  P,  plus  the  resistance  of  its  inertia.  Or  the 

compressional  force  is  P +m  — ,  where  m  is  the  mass  of 

dt 

the  lamina.     The  work  of  compression  will  therefore    be 


—  \dc. 


MECHANICS  13 


On  lamina   4,    this    work   will    be 


P  +  m  —  jdc*  =  PC  4  4-  —  ^-  ,  where  v*  represents  the 
dt  '  2 

velocity  of  the  lamina  at  the  instant  we  are  considering, 
with  corresponding  expressions  for  the  other  laminae. 
Hence,  designating  the  potential  energy  at  any  point,  at 
any  instant,  by  W,  and  the  kinetic  energy  by  T,  we  have 
W  =  PC  +  T.  Or  the  potential  energy  is  equal  to  the 
normal  pressure  into  the  distance  the  lamina  has  been 
compressed,  plus  its  kinetic  energy.  In  other  words,  the 
kinetic  energy  of  a  lamina  is  equal  to  the  work  of  compres- 
sion done  upon  it  in  excess  of  the  work  done  by  the  normal 
pressure.  The  wave  set  up  before  such  a  single  thrust  is 
known  as  a  compressional,  or  positive,  wave.  It  travels 
along  with  a  uniform  velocity,  compressing  and  moving 
along  successively  all  parts  of  the  medium  in  its  path, 
and  leaving  them  at  rest,  but  set  down  at  a  certain  definite 
distance  from  their  original  position,  viz.,  the  distance,  or 
amplitude,  of  the  thrust. 

Referring  again  to  Fig.  1,  it  will  be  seen  that  while  the 
medium  to  the  right,  against  which  the  thrust  was  made, 
transmits  a  compressional  wave  with  uniform  velocity 
in  the  direction  of  the  thrust,  the  medium  to  the  left,  away 
from  which  the  thrust  was  made,  will  equally  transmit 
an  expansional  wave,  towards  the  left.  And  by  the  same 
reasoning  as  before,  the  work  of  expansion  at  any  point 
will  be  equal  to  the  kinetic  energy  at  that  point,  plus  the 
work  done  against  the  normal  pressure  during  the  ex- 
pansion. In  either  case,  we  have  the  formula  W  =  PC  -f  T. 

If  we  thrust  the  lamina  1  forward  and  backward, 
always  through  the  same  limits,  we  have  what  is  called  a 
vibrational  wave.  After  one  complete  excursion  forward 
and  back,  it  is  evident  that  no  work  will  have  been  done 


by  the  normal  pressure,  or         dc  =  o.    Hence  the  term  PC 


14 


ELECTRICAL 


vanishes,  and  for  a  complete  or  finished  vibration,  the 
total  potential  energy  of  the  wave  will  be  equal  to  the 
total  kinetic  energy.  The  average  kinetic  energy,  or  the 
average  potential  energy,  is  half  of  its  maximum  value. 
Hence  the  whole  energy,  if  represented  by  a  single  form, 
would  be  equal  to  the  maximum  value  of  that  form  dis- 
tributed throughout  the  whole  wave.  As  *Lord  Rayleigh 
puts  it  "In  a  progressive  wave  of  any  type  one-half  of  the 
energy  is  potential  and  one-half  is  kinetic.  The  total 
energy  of  the  wave  is  equal  to  the  energy  derived  £rom 
compressing  its  whole  mass  from  its  minimum  to  its 
maximum  density,  or  to  the  energy  of  the  whole  mass 
moving  with  its  maximum  velocity." 

This  is  an  important  general  principle  in  nature,  viz., 
that  where  no  hindrance  is  opposed,  or  where  two  kinds 
of  energy  are  free  to  change  or  flow  into  each  other, 
they  always  become  equal.  The  wave  contains  a  certain 
definite  quantity  of  energy  divided  into  two  parts.  The 
potential  energy  always  strives  to  release  itself  into 
kinetic  energy,  but  when  an  equalization  has  been  effected, 
no  more  potential  energy  can  flow  into  kinetic  energy, 
and  vice  versa,  since  no  form  of  energy  can  rise  above  its 
source. 

The  intimate  structure  of  a  longitudinal  vibrational 
wave  is  shown  in  Fig.  2. 


*  Lord  Rayleigh.     Theory  of  Sound.     Par.  245. 


MECHANICS  15 

The  equal  laminae  in  the  lower  part  represent  the 
medium  at  rest,  and  the  upper  part  shows  the  transposition 
and  compression  of  these  same  laminae  at  a  certain  instant 
during  the  passage  of  a  wave  The  dotted  curve  repre- 
sents graphically  the  density  at  different  points,  the  com- 
pression or  rarefaction  being  proportional  respectively  to 
its  height  above  or  below  the  line  A  B.  The  positions  of 
the  prong  of  a  tuning  fork  corresponding  to  the  several 
points  of  the  wave  are  shown  below.  The  laminae  in  the 
forward  or  rarefactional  part  of  the  wave  are  moving 
backward,  while  the  laminae  in  the  rearward  half  are  all 
moving  forward,  as  indicated  by  the  small  arrows.  The 
distance  a,  or  the  extreme  distance  which  a  particle  moves 
on  either  side  from  its  position  of  equilibrium,  is  called  the 
amplitude  of  the  wave.  The  extreme  lamina/1  has  just 
come  to  rest  and  its  normal  density,  after  swinging  forward 
through  the  amplitude  a,  and  is  just  preparing  to  swing 
back.  Its  subsequent  positions  relatively  to  its  position 
of  equilibrium,  and  its  density,  are  shown  by  the  successive 
laminae  in  the  rear.  The  disturbance  is  supposed  to  be 
progressing  towards  the  right,  as  shown  by  the  large  arrow, 
having  originated  at  some  point  to  the  left.  But  it  is 
possible  for  a  wave  to  proceed  outward  from  a  disturbance 
with  its  compressed  parts  moving  backward,  and  its  rare- 
fied parts  moving  forward.  Thus  if  we  had  a  membrane 
containing  a  compressed  gas,  with  a  vibrating  body  in  the 
interior  giving  off  waves  with  the  compressed  halves 
moving  outward,  we  should  expect  the  waves  leaving  its 
surface  to  have  the  motions  of  their  respective  halves 
reversed.  For  the  compressed  half,  when  passing  through 
the  membrane  escapes  into  a  rarer  medium  and  expands 
suddenly,  while  the  expanded  half  moving  backward, 
towards  the  membrane,  does  so  against  a  higher  pressure 
and  should  be  compressed.  On  the  other  hand,  if  the 
pressure  within  the  membrane  is  lower  than  that  of  the 
outside  medium,  the  motion  of  the  respective  halves 


16  ELECTRICAL 

should  be  unaltered.  In  both  cases  the  waves  proceed 
regularly  outward,  away  from  the  disturbing  body,  but 
with  this  peculiar  difference,  viz.,  that  the  directions  of 
the  motion  of  their  compressed  and  rarefied  halves  are 
reversed.  We  shall,  conventionally,  define  a  wave  with 
its  compressed  portions  moving  away  from  the  disturbing 
source,  as  a  positive  wave;  and  a  wave  with  its  condensed 
parts  moving  towards  the  disturbing  source  as  a  negative 
wave.  A  single  compressional  wave,  due  to  a  unidirec- 
tional thrust  (explosion)  has  sometimes  been  called  a 
positive  wave,  and  a  single  unidirectional  expansive  wave 
has  accordingly  been  termed  a  negative  wave.  Our 
definition  above,  however,  applies  only  to  bidirectional, 
or  vibratory,  waves. 

If  we  should  expand  one-half  of  a  wave  from  its  original 

length  -  ,  where  /  is  the  length  of  the  wave,  to  its  actual 

length  in  the  expanded  half,  which  is  -  +  2a,  and  should 
likewise  compress  the  other  half  from  its  original  length 

-  to  its  actual  length 2a,  the  energy  so  expanded  would 

clearly  be  equal  to  the  compressional  or  potential  energy 
of  the  wave.     The  work  of  expanding  -  to  — \-  2a  is,  since 

JL        JL 

the  pressure  is  inversely  as  the  volume,  or  p  «=  P 


l+2c 
where  c  is  the  expansion,  W 


Developing  the  logarithm  by  Maclaurin's  theorem,  and 
neglecting  higher  powers  of  a,  since  the  amplitude  is 

4  Pa2 
supposed    to    be    small,   we  have    W  =  —  2  Pa  -\  --  . 


MECHANICS  17 


Likewise  the  work  of  compression,  from  a  length -to  a 


length 2a,  isW=2Pa  + .      The  total   potential 

energy  in   the   wave   is,    therefore,  .      Considering 

a  unit  cross  section  of  the  wave,  its  mass  is  Dl,  where  D 
is  the  normal  density  of  the  medium.  Let  v  be  the  average 
velocity  of  a  lamina  during  a  complete  vibration.  Then 
since  a  lamina  traverses  a  distance  4a  while  the  wave 
progresses  a  wave  length,  /,  and  designating  the  velocity 

of  the  wave  by  V,  we  have  v  = .     The  total  kinetic 


energy  of  the  wave  is  ^"~    = .     But  this  must  be 

equal  to  the  total  potential  energy.     Hence  V  =^l  _. 

There  is  a  difference  between  a  gaseous  medium  and  the 
ether  in  that  the  molecules  take  up  a  part  of  the  space 
and  the  compression  is  not  actually  measured  by  the  ratio  of 

2a  to  -  .     The  formula  for  a  gas  becomes  V  =  */  k  —  , 

where  k  is  the  ratio  of  the  two  specific  heats.  (See  "The  At- 
mosphere," by  the  author.)  The  motion  of  the  molecules 
of  gross  matter  constitutes  the  phenomenon  of  heat,  and 
since  the  ether,  as  far  as  we  know,  is  a  continuous  medium, 
such  a  thing  as  heat  is  foreign  to  its  nature.  The  ether 
can  be  neither  hot  nor  cold,  although  it  transmits  vibrations 
from  gross  matter  which  render  other  bodies  hot  or  cold. 

The  formula  V  =  ^       is  an  important  one  for  all  media. 

It  must  be  remembered  that  it  holds  only  where  the  am- 
plitudes are  so  small  that  powers  above  the  square  may  be 


18  ELECTRICAL 

neglected.  Where  the  amplitudes  are  so  great  that  higher 
powers  cannot  be  neglected,  the  velocity  of  propagation  of 
a  disturbance  may  be  very  much  greater.  Thus  in  the  air, 
violent  unidirectional  disturbances,  such  as  explosions, 
may  be  propagated  with  very  high  velocities,  the  velocity 
increasing  with  the  intensity  and  suddenness  of  the  thrust. 
The  same  is  true  of  the  ether,  and  the  standard  velocity, 

V  =3  X1010 1,  holds  good  only  for  longitudinal  waves 

sec. 

of  small  amplitude.  Disturbance  can  be  propagated  with 
a  much  higher  velocity,  although  not  with  a  lower  velocity 
in  the  case  of  longitudinal  waves. 

We  have  said  that  the  ether  is  without  viscosity:  it  is 
frictionless.  But  when  a  stream  or  current  of  ether 
impinges  upon  an  impermeable  surface,  it  must  exercise 
a  pressure  upon  such  a  surface.  It  flows  freely  between 
and  through  molecules,  but  not  through  atoms.  The  space 
occupied  by  atoms  is  not  occupied  by  ether,  and  the  ether 
must  flow  around  such  bodies. 

We  shall  assume  that  the  pressure  exerted  on  a  surface 
S  is  proportional  to  the  density  of  the  ether  current,  and 
to  the  velocity  with  which  the  current  is  flowing,  so  that 
we  may  write  p  =  vDS.  When  a  current  of  ether  is 
flowing  in  a  conductor  it  has  to  make  its  way  past  the 
atoms  and  thus  exerts  a  pressure  upon  them.  A  counter 
pressure  is  equally  exerted  upon  the  current  which  is 
thus  resisted  to  this  extent.  Let  us  call  the  electro-motive 
force,  or  the  driving  pressure,  or  the  pressure  gradient,  E. 
The  current  starts  from  zero  velocity  and  rapidly  increases 
its  velocity.  Calling  the  mass  of  ether  which  flows 
through  a  cross  section  of  the  conductor  in  unit  time  m, 

//7J 

we   have    E  —  p  =  E  —  vDS  =  m  — .      The    current    will 

dt 

increase  until  the  resulting  driving  force,  or  the  accelera- 
tion becomes  zero.  When  this  point  is  reached,  the 


MECHANICS  19 

velocity  of  the  current  becomes  uniform.  The  condition 
for  such  a  state  is  E  =  vDS.  Let  us  call  the  back  pressure, 
or  resistance,  when  unit  mass  of  ether  is  flowing  in  unit 
time,  R.  The  value  of  R  will  naturally  depend  on  the 
total  atomic  surface  opposing  the  flow,  and  will  be  differ- 
ent for  different  substances.  We  can  write  our  condition, 

^ 

then,    E  =  vDR  or  vD  =  — .     But    vD    is    the    mass    or 

R 

quantity  of  ether  which  is  flowing  through  a  cross  section 
of  the  conductor  in  unit  time,  and  this  measures  the 
current  strength.  Calling  the  quantity  of  ether  flowing 

r? 

in  unit  time  C,  we  have   C  =  — ,    which  is  Ohm's   law. 

R 

This  law  confirms  exactly,  experimentally,  our  assumption, 
then,  that  p  =  vDS.  Ohm's  law  not  only  states  the 
axiom  that  when  a  current  is  constant,  or  flowing  with  a 
uniform  velocity,  it  has  no  acceleration,  but  it  also  states 
that  the  resistance  is  proportional  to  the  quantity  or  mass 
of  ether  flowing  in  unit  time.  The  resistance  thus  meas- 
ures a  velocity  as  well  as  a  density.  Theoretically  the 
condition  of  equilibrium  would  never  be  reached.  Prac- 
tically it  is  reached  in  a  very  short  time.  The  driving 
force  of  the  current  does  work  in  overcoming  the  re- 
sistance offered  by  the  atomic  surfaces.  In  overcoming 
this  resistance  it  sets  the  atoms  into  vibration  about  their 
positions  of  equilibrium,  with  the  result  that  the  energy 
of  the  current,  which  is  EC,  becomes  transformed  into 
kinetic  energy  of  the  atoms  (molecules).  In  a  fluid  con- 
ductor (mercury),  this  pressure  results  in  visible  motion, 
as  seen  in  electro-capillary  phenomena.  C  representing 
the  mass  of  ether  flowing  in  unit  time,  the  atomic  kinetic 
energy,  or  the  heat  developed,  is  proportional  to  ECt, 
which  is  known  as  Joule's  law. 

Returning  to  Fig.  2,  it  is  evident  that  the  velocity  of 
the  flow  of  the  expanded  ether  in  the  wave  must  be 


20  ELECTRICAL 

slightly  greater  than  that  of  the  compressed  ether.  It  is 
further  evident  that  the  average  velocities  in  the  two 
halves  must  be  inversely  as  the  densities.  Thus  the  con- 
densed ether  in  the  compressed  half  flows  a  little  more 
slowly  than  the  rarer  ether  in  the  expanded  half;  but  as 
the  pressure  exerted  upon  a  surface  is  proportional  to 
the  density  and  the  velocity,  we  are  led  to  the  important 
result  that  the  average  pressures  exerted  upon  a  surface 
are  the  same  in  both  halves. 

Let  us  suppose  that  a  particle  denser  than  the  ether 
is  in  the  path  of  a  longitudinal  wave.  As  the  condensed 
half  of  the  wave  sweeps  over  it  it  will  urge  the  particle 
forward.  Let  v  be  the  average  velocity  of  the  ether 
particles,  and  vl  the  average  velocity  of  the  denser  particle 
during  the  passage  of  the  condensed  half  of  the  wave. 
Evidently  the  denser  particle  will  lag  behind  the  ether 
particles.  We  shall  assume  that  Dv  =  Z)V,  where  D 
and  D1  are  the  respective  densities,  or  the  average  velocities 
will  be  inversely  as  the  densities.  Let  5  be  the  distance 
which  the  denser  particle  has  moved,  while  an  ether 
particle  has  moved  2a,  thus  completing  a  half  wave.  If 
M  is  the  mass  of  the  denser  particle,  and  m  the  mass  of  an 
equal  volume  of  ether,  then  Ms  =  2am.  Their  distance  apart 

at  the  end  of  a  half  swing  will  be,  therefore,  '* 


M 

Likewise,  on  the  backward  swing,  the  denser  particle  and 
a  corresponding  mass  of  ether,  starting  from  rest,  will, 
at  the  end  of  the  swing  be  the  same  distance  apart.  Or 


the   denser  particle  always   lags  a  distance    2 a 


behind  the  corresponding  ether  particle.     The  time  taken 

by  each  half  wave  to  clear  the  ether  particle  is — ,  while 

2V 


MECHANICS  21 

the  time  taken  by  the  compressed  half  to  clear  the  denser 

particle  is  —  — -,  and  the  time  taken  by  the 

2V  MV 

expansional  half  to  clear  the  denser  particle  is 

l_        la  (M—m) 

2V  MV 

The  current  pressure,  therefore,  which  is  D^,  acts  for  a 
shorter  time  upon  the  denser  particle  during  the  passage 
of  the  condensed  half,  and  for  a  longer  time  during  the 
passage  of  the  expanded  half.  It  is  evident  that  the 
pressure  gradient  which  is  equal  on  both  sides  and  acts 
for  the  same  time  can  have  no  effect.  The  net  result, 
then,  is  that  a  backward  pressure,  equal  to  DV,  acts  for 

4a(M— m)    ,     . 

a  time  equal  to   during  the  passage  of  every 

MV 

complete  wave.  This  will  be  equivalent  to  a  backward 
acceleration,  acting  continuously,  of 

Dy      4a(M— m) 
~T  MV 

where  t  is  the  time  of  a  complete  vibration. 

Dv   4a  (M—m)  16a2      (M—m)  4a  (M—m) 

_  ,  •  —    j_)  • •    =   iJ'O  •  . 

MVt  I  Mt  Ml 

Measuring  the  density  of  the  ether  by  its  pressure,  P, 

,,dv  P16a*          (M—m)  E(M—m) 

we   have   M—      =     .     - '      =     — -, 

dt  I  Mt  Mt 

where  E  is  the  total  energy  in  a  complete  wave  per  unit 

cross  section.     We  have  already   seen  that  E  =  P . 


22  ELECTRICAL 

If  M  <  w,  the  acceleration  becomes  reversed,  and  we 
see  that  a  body  less  dense  than  the  ether  will  be  urged 
forward  in  the  direction  of  the  motion  of  the  condensed 
half.  This  is  evident,  since,  in  this  case  the  compressed 
half  will  act  upon  the  body  longer  than  the  expanded  half 

by  a  time  equal  to    -— — ..      If  the  particle  consists 

MV 

of  matter  very  much  denser  than  the  ether,  as  is  the  case 

with  all  gross  matter,  the  fraction,  -       — ,  becomes  prac- 

M 

77 
tically  unity,  and  the  force  will  be   — .     Every  atom  of 

gross  matter,  therefore,  which  sends  out  positive  longi- 
tudinal waves,  and  these  are  the  only  kind  of  longitudinal 
waves  which  atoms  are  capable  of  radiating,  will  attract 

^ 
every  other  atom  with  a  force  —  S,  where  5  is  the  surface 

of  the  attracted  atom. 

If  the  waves  radiate  from  a  spherical  surface  Si,  — Si 

measures  the  flow  of  energy  from  its  surface  in  unit  time, 
and  this  flow  through  all  other  concentric  spherical  sur- 
faces remains  constant.  Hence  the  attraction  of  such  a 
body  on  all  spherical  shells  surrounding  it  is  constant, 
and  equal  to  the  total  outflow  of  energy  in  unit  time. 

Since  every  atom  in  an  attracting  body  sends  out  such 
waves,  the  total  attraction  will  be  proportional  to  the 
mass  of  the  body,  and  since  the  total  surface  of  the  atoms 
acted  upon  in  the  attracted  body  is  proportional  to  the 
number  of  atoms,  or  to  its  mass,  the  total  attraction  is 

MM1E 
proportional  to  . 


MECHANICS  23 

Since  the  total  wave  energy  flowing  through  any 
spherical  surface,  surrounding  the  disturbing  source, 
in  unit  time,  remains  constant,  the  wave  energy  at  any 
point,  or  its  intensity  per  unit  of  surface,  varies  inversely 
as  the  square  of  the  distance.  Hence,  the  attraction  of  a 

MM1      E 
body  on  a  distant  body  is  proportional  to  .  — ,  where 

r  is  the  distance  between  them.  This  is  Newton's  law. 
We  have  kept  the  term  attraction  because  it  is  sanctioned 
by  long  usage,  but  it  must  be  remembered  that  in  nature 
there  is  no  such  thing  as  a  drawing  of  bodies  together. 
It  is  a  "vis  a  tergo,"  or  a  pushing  together,  the  forces  being 
applied  to  the  surfaces  of  the  atoms. 

If  the  attracted  body  is  dead,  i.e.,  not  sending  out  any 
waves,  it  can  exert  no  attraction,  but  is  simply  attracted. 
If  both  bodies  are  alive — radiating  waves — their  attrac- 

MM1   E      .MM1   El 
tions  on  each  other  are  respectively .  —  and .  —  . 

Where  E  =  E1  and  t  =  tl,  the  mutual  attractions  are 
equal.  Both  the  wave  energy  sent  out  by  a  vibrating 
atom,  and  the  action  of  such  waves  on  an  atom  are  pro- 
portional to  their  surfaces,  or  cross  sections.  Whether 
all  atoms  radiate  waves  of  the  same  frequency  and  con- 
taining the  same  amount  of  energy  per  unit  of  radiating 
surface,  we  do  not  know.  If  their  motion  (vibration)  is 
derived  from  the  internal  motion  of  the  ether,  as  seems 
possible,  such  would  be  the  case.  We  should  have  a 
case,  then,  analogous  to  the  Brownian  vibrations  seen  in 
small  material  particles  suspended  in  a  liquid,  where  the 
invisible  internal  motion  of  the  molecules  becomes  visible 
in  the  larger  particles.  We  shall  see  that  the  motion  to 
and  fro  of  an  atom  results  in  the  radiation  of  an  electro- 
magnetic, or  heat,  wave,  and  a  longitudinal  wave  at  right 
angles  to  it.  If  such  stronger  longitudinal  waves  are  the 


24  ELECTRICAL 

only  ones  participating  in  attraction  we  should  expect  the 
attraction  to  be  a  function  of  the  temperature  of  a  body, 
so  that  a  body  at  the  absolute  zero  would  be  attracted 
but  could  not  attract.  But  of  all  these  matters  we  are  in 
complete  ignorance.  It  is  to  be  remarked,  however,  that 
the  energies  radiated  by  the  two  kinds  of  waves  are  not 
equal  and  that  with  increasing  frequencies  of  the  vibrations 
the  energy  passes  off  almost  exclusively  in  electro-magnetic 
waves. 

Where  M<C  m,  we  have  seen  that  there  is  repulsion 
instead  of  attraction.  Since  in  this  case,  the  bodies  acted 
upon  have  a  density  less  than  that  of  the  ether,  their 
inertia  is  very  slight  and  they  are  driven  almost  imme- 
diately to  their  limiting  velocity,  which  is  that  of  the  wave 
itself.  Comets'  tails  and  the  corona  of  the  sun  must 
represent  some  form  of  extremely  tenuous  matter,  since 
they  are  repelled  with  the  velocity  of  light. 

If  the  attracted  body  is  moving,  then  a  Doppler  effect 
will  result.  If  moving  against  the  waves,  then  more 
waves  will  pass  it  in  a  given  time,  and  the  frequency  will 
be  raised  factitively.  t  will  become  relatively  smaller 
and  the  attraction  increases.  If  the  attracted  body  is 
moving  with  the  wave,  for  the  same  reason  the  attraction 
will  become  less.  But  the  frequency  of  all  longitudinal 
waves  in  the  ether  is  so  extremely  high,  that  a  few  miles 
more  or  less  of  relative  velocity  is  wholly  negligible.  The 
greatest  velocities  so  far  observed  for  dense  matter  among 
the  heavenly  bodies  hardly  exceeds  200  miles  per  second. 
Compared  with  the  enormous  velocity  of  wave  propaga- 
tion, viz.,  186,000  miles  per  second,  this  is  insignificant. 

We  have  seen  that  the  attraction  exerted  by  a  wave 

E'er 

upon  an  atom  is  — --  .     Since  we  find  that  different  kinds 

of  atoms  have  different  "weights"  or  are  acted  upon  more 
strongly  by  the  same  waves,  they  must  have  different 


MECHANICS  25 

average  cross  sections.  A  priori  it  would  be  highly  im- 
probable that  all  atoms  should  have  the  same  average 
cross  section.  Hence,  we  are  justified  in  inferring  that, 
since  their  atomic  weights  vary  through  a  range  of  from 
1  to  238,  their  average  cross  sections  must  vary  through 
a  like  range,  and  their  linear  dimensions  must  vary  through 
a  range  of  from  1  to  16.  But  we  are  not  justified  in  infer- 
ring anything  as  to  their  size  or  shape,  or  anything  else 
beyond  this. 

Possibly,  if  it  is  true,  as  is  generally  believed,  that  in 
the  crystalline  state,  atoms  arrange  themselves  symmetri- 
cally, and  if  it  were  found  that  crystals  weighed  more  when 
pointed  in  one  direction  than  in  another,  we  might  infer 
that  their  dimensions  in  one  direction  were  greater  than 
in  another.  But  nothing  of  the  sort  has  ever  been  found, 
or  even  tried. 

We  may  sum  up  the  results  so  far  obtained  as  follows: 
The  attraction  and  repulsion  of  bodies  at  a  distance,  such 
as  is  everywhere  observed,  can  only  take  place  through  a 
medium.  Without  a  medium,  no  action  at  a  distance 
would  be  possible.  Various  actions — gravitational,  elec- 
trical, magnetic,  etc. — are  effected  without  the  interposi- 
tion of  gross  matter,  and  it  is  certain  that  these  actions 
are  transmitted  through  the  ether.  Motion  can  only  arise 
from  motion:  hence  these  actions  are  transmitted  by 
motion  of  some  kind  in  the  ether.  All  motions  that  are 
possible  in  a  medium  do  occur.  The  only  possible  motions 
in  a  fluid  medium  are  three. 

1 .  Translational  motion,  or  a  streaming  of  the  medium. 
We  can  effect  motion  at  a  distance  by  striking  an  object 
with  a  projectile. 

2.  A  peculiar  kind  of  alternate  streaming  in  opposite 
directions,  constituting  longitudinal  waves.     We  have  seen 
that  such  a  motion  is  capable  of  effecting  attractions  and 
repulsions. 

3.  Vortex  motion.     We   shall   examine  this  form  of 


26  ELECTRICAL 

motion,  which  consists  of  streaming  in  closed  curves, 
directly.  We  shall  see  that  while  this  form  of  motion  is 
capable  of  causing  attractions  and  repulsions  of  a  peculiar 
nature,  which  we  recognize  as  magnetic,  they  are  incapable 
of  causing  the  general  attractions  and  repulsions  with 
which  we  are  familiar.  As  stated  before,  we  have  omitted 
a  general  vortex  motion  of  the  ether,  not  in  closed  curves, 
such  as  possibly  has  led  to  the  formation  of  celestial  sys- 
tems (spiral  nebulae  and  solar  systems),  as  not  lying  within 
our  present  scope. 

Hence  gravitational  attraction  must  be  due  to  longi- 
tudinal waves.  Since  the  amount  of  wave  energy  flowing 
through  a  closed  surface  remains  constant,  its  concentra- 
tion, or  intensity,  is  inversely  proportional  to  the  square  of 
the  distance.  Whence  Newton's  law  follows,  viz.,  the 
attraction  between  two  bodies  is  proportional  to  the 
product  of  their  masses,  and  inversely  proportional  to 
the  square  of  the  distance  between  them. 

ES 

The  wave  force  — ,  which  includes  both  attraction  and 
t 

repulsion,  may  perhaps  best  be  called  the  differential 
inertianal  pressure.  Gravitational  pressure  implies  gross 
matter,  but  we  shall  see  that  condensed  and  rarefied  ether 
is  equally  subject  to  this  force.  We  shall  find  that  a  mass 
of  condensed  ether,  or  a  positive  charge  of  electricity, 
gives  off  only  negative  waves,  while  a  mass  of  rarefied 
ether,  or  a  negative  charge  of  electricity,  gives  off  only 
positive  waves.  Hence  all  gross  matter  attracts  all  other 
gross  matter  and  all  masses  of  condensed  ether,  while 
repelling  all  masses  of  rarefied  ether.  On  the  other  hand 
condensed  ether  repels  condensed  ether  and  attracts 
rarefied  ether,  while  rarefied  ether  repels  rarefied  ether  and 
attracts  condensed  ether. 


VORTEX  FILAMENTS 
IN  THE  ETHER 


In  all  elastic  fluids,  vortex  filaments  are  readily  formed. 
The  condition  is  simply  that  a  rotating  sheet  of  the  fluid 
shall  by  its  centrifugal  force  support  the  excess  of  pressure 
of  the  general  medium  over  the  lessened  pressure  in  the 
interior.  In  a  gas,  friction  soon  reduces  the  rotational 
energy  of  the  sheet,  so  that  they  cannot  long  persist:  but 
in  the  ether,  which  has  no  viscosity,  such  vortices  persist 
indefinitely  and  would  persist  forever  unless  destroyed 
under  special  conditions  which  we  shall  investigate  later. 
In  an  incompressible  liquid,  and  all  liquids  are  little  com- 
pressible, apart  from  friction,  the  formation  and  persist- 
ance  of  linear  vortices  is  rendered  difficult  because  the 
necessary  lessened  pressure  in  the  interior,  which  holds  the 
outer  rotating  sheet,  can  hardly  be  attained  short  of  a 
complete  vacuum  in  the  axis.  In  a  gaseous  medium  a 
linear  vortex  need  not  be  a  closed  curve,  provided  its  two 
ends  are  shut  off  by  surfaces  impermeable  to  the  medium ; 
but  in  the  ether  such  linear  vortices  always  form  closed 
complete  rings. 

Such  vortex  rings  are  very  familiar  to  us.  A  locomotive 
puffs  them  out  of  its  smoke  stack,  and,  when  they  are 
accompanied  by  smoke,  they  are  visible;  otherwise  not. 
Smokers  learn  how  to  blow  them.  They  accompany  the 
blast  of  a  gun;  visible  with  black  powder;  invisible  with 
smokeless.  They  are  easily  made  by  tapping  smoke  out 
of  a  box  through  a  circular  orifice.  This  formation  is  not 
to  be  explained  as  due  to  the  friction  of  the  gas  on  the 

27 


28  ELECTRICAL 

edges  of  the  orifice.  All  gases,  of  course,  are  subject  to 
friction,  but  this  is  very  slight.  It  is  due  to  a  stoppage 
and  diversion  of  the  currents  at  and  in  the  vicinity  of  the 
edge,  while  the  central  stream  flows  on  unobstructed. 
Certain  currents  at  the  edges  are  stopped  and  even  begin 
to  flow  backward.  A  line  of  lessened  pressure  forms,  and 
the  central  streams  are  pushed  back  over  this  and  by  their 
momentum  are  carried  around  it.  Once  formed,  it  must 
persist,  unless,  as  in  the  case  of  gases,  its  energy  is  used 
up  by  friction.  In  a  conductor  the  molecules  are  more 
densely  packed  together  near  the  surface  than  in  the 
interior.  This  is  especially  marked  at  the  surface  where 
a  peculiar  differentiated  condition  exists  which  is  known 
as  a  "surface  tension."  The  mutual  attraction  of  the 
molecules  is  here  all  towards  the  interior  with  no  counter- 
balancing action  from  the  exterior.  In  the  centre,  the 
attractions  oppose  each  other  from  all  directions  so  that 
here  the  density  and  tenacity  are  least.  It  is  for  this  rea- 
son that  a  wire  cable  is  much  stronger  than  a  rod  of  the 
same  material  of  equal  cross  section.  The  flow  of  a  steady 
electric  current  is  greater  in  the  axis  of  a  conductor  than 
in  the  peripheral  portions.  Hence  we  have  a  condition 
favorable  to  the  formation  of  vortices.  The  current  is 
less  obstructed  in  the  centre,  and  more  obstructed  in  the 
peripheral  portions,  so  that  it  is  natural  to  expect  that 
vortex  rings  of  ether  will  be  thrown  off  surrounding  the 
conductor.  And,  in  fact,  we  find  that  whenever  a  current 
is  flowing  in  a  conductor,  it  is  always  surrounded  by  such 
vortex  rings.  Further  such  rings  are  always  rotating  in 
such  a  direction  that  the  inner  edge  of  the  ring  moves  in 
the  direction  of  the  current  which  formed  it,  while  the 
outer  edge  moves  in  the  opposite  direction. 

A  small  length  of  a  vortex  filament  may  be  regarded 
as  a  cylinder  made  up  of  an  infinite  number  of  concentric 
cylindrical  sheets,  each  rotating  with  an  angular  velocity, 
G>.  The  pressure  at  the  surface  is  the  normal  ether  pres- 


MECHANICS  29 

sure,  P.  The  increment  of  pressure  outward  from  the 
axis,  due  to  the  centrifugal  force,  is  dp  =  pdr .  ra)*.  The 

density,   p  =  — .     Hence  log  -£*    =       -   I  r2 — a8)  1,  a 

being  the  radius  of  the  cylinder.  The  pressure  falls 
logarithmically  from  the  surface  to  the  axis,  the  fall 
increasing  as  the  square  of  the  angular  velocity. 

Let  us  suppose  that  the  original  whirl  imparted  to  the 
vortex  was  violent  enough  to  cause  a  complete  vacuum 
in  the  axis,  or  the  filament  consists  of  a  current  sheet 
surrounding  a  complete  vacuum.  The  normal  pressure 
of  the  current  sheet  is  P  at  every  point,  and  therefore  the 
filament  cannot  collapse  about  its  axis,  but  there  is  also  a 
lateral  pressure,  P,  which  is  unsupported,  and  which 
therefore  tends  to  expand  the  circumference  of  the  ring. 
The  absolute  potential  energy  of  the  current  sheet,  or  its 
potential  energy  measured  from  an  absolute  zero,  is  half 
its  pressure  into  its  volume.  Taking,  ht  as  the  thickness 
of  the  sheet,  and  5  as  its  surface,  its  total  potential  energy 

PSh       Pu 

is   =  — ,  where  u  is  the  volume  of  the  sheet.    Now 

2  2 

the  moment  of  momentum  of  the  sheet,  or  wr2<w,  will 
remain  constant,  but  the  thickness  of  the  sheet,  h,  and  r 
will  diminish  as  the  ring  expands.  However  the  volume 

of  the  sheet  u,  and  its  total  potential  energy   — ,    will 

remain  constant.  This  potential  energy  tends  to  expand 
the  ring  and  thereby  to  impart  kinetic  energy  to  it  as  a 
whole.  It  does  not,  however,  lose  its  energy  by  so  doing, 
since  it  is  automatically  kept  at  a  constant  point,  by 
drawing  from  the  rotational  energy  whatever  it  loses  as 
kinetic  energy.  It  is  evident  that  when  the  kinetic  energy 
of  the  ring  becomes  equal  to  the  potential  energy  of  the 


30  ELECTRICAL 

sheet,  a  condition  of  equilibrium  will  have  been  reached, 
and  there  is  no  further  exchange  between  the  energies. 


At  this  point =  — ,  or  V  =  -u—    =  -\J —  ,  and 


we  see 


u 


that  the  ring  will  spread  out  with  the  standard  velocity. 

This  is  on  the  supposition  that  its  flight  is  unresisted. 
We  have  seen  that  any  body  moving  through  the  ether 
must  be  resisted  by  an  amount  proportional  to  the  velocity 
with  which  it  moves,  and  to  the  surface  which  it  opposes. 
A  single  ring,  therefore,  no  matter  with  what  velocity  it 
is  thrown  out,  must  soon  come  to  rest,  or  move  so  slowly 
that  the  resistance  it  experiences  does  not  overcome  the 
expansive  effort  of  the  potential  energy.  However,  in 
opposing  the  resistance,  it  throws  up  a  compression  wave 
in  front  and  an  expansion  wave  behind,  and  these  longi- 
tudinal waves  travel  ahead  with  the  standard  velocity. 
If  the  foremost  ring  is  lagging,  it  is  overtaken  by  these 
waves  from  the  rings  which  have  been  given  off  subse- 
quently, and  since  it  is  a  body  less  dense  than  the  ether, 
it  will  be  urged  on  by  these  waves  and  quickly  take  their 
step.  The  result  is  that  all  the  rings  will  almost  immedi- 
ately be  moving  out  with  their  natural  velocity,  as  if  they 
were  unresisted,  and  in  fact  they  are  unresisted  for  the 
effect  of  the  longitudinal  waves  which  they  set  up  is  to 
cause  the  ether  to  move  with  them  at  the  standard  velocity. 

The  ring  cannot  collapse  about  the  axis  of  the  filament 
because  the  pressure  of  the  external  ether,  P,  is  balanced 
at  every  point  of  its  surface  by  an  equal  and  opposite 
centrifugal  force.  There  is,  however,  a  differential  ex- 
ternal pressure  tending  to  compress  the  ring  into  a  smaller 
circle.  For  calling  the  distance  from  the  centre  of  the 
ring  to  the  axis  threading  the  filament,  R,  and  the  radius 
of  a  cross  section,  r,  let  us  cut  the  ring  into  two  parts  by 
a  vertical  cylinder  passing  through  the  axis  of  the  filament. 


MECHANICS  31 

The  component  of  the  surface  parallel  to  the  cylinder  on 

+r  +r 

the  inner  side  is  2n  \  (R—  x)  dy  =  2ir  \  (R—  Vr*—y*)  dy 


—  7T2r2.  Likewise  the  component  of  the  outer 
surface  parallel  to  the  cylinder  is  ^irrR  +  TT*r*.  Hence 
the  differential  pressure  inward  is  2  P7T2r2. 

Taking  the  case  of  a  vortex  with  a  central  vacuum 
where  the  expansional  pressure  of  the  current  sheet  is  P, 
this  is  equivalent  by  Laplace's  formula  to  a  radial  pressure 

p 

outward  of  —  .     The  total  amount  of  this  pressure  outward 
R 

p 

is  evidently  —  .  ^irrR  =  P  .  4irr.     Where  r  is  so  small 
R 

that  we  can  neglect  its  square  in  comparison  with  its  first 
power,  the  differential  external  pressure,  2P7T2r2,  is  neg- 
ligible. But  when  a  vacuum  does  not  exist  in  the  axis, 
and  the  average  pressure  of  the  sheets  is  below  P  and 
r  comparatively  large,  it  is  evident  that  a  position  will 
generally  be  found  where  the  expansional  pressure  will  be 
exactly  balanced  by  the  differential  external  pressure,  and 
in  this  position  the  ring  will  remain  stationary. 

In  a  vortex  filament  with  a  central  vacuum  the  centri- 
fugal force  per  unit  of  surface  must  equal  the  external 
pressure.  The  surface  of  the  ring  is  ^ir^rR  and  its 
volume,  U,  is  27T2r2R.  Hence 


r,         -  nn  ~>        T->  TT      mvz 
mpt  and— ^-   =  P[/  =  — , 

where    v    is    the    velocity    of    the    current    sheet.      Or 

/2P          /2P 
fl  =  *y —  =  ^ — -.     Dl  is  the  average  density  of  the  ring, 

u 
and  is  less   than   that  of  the  normal  ether.     The   velo- 


32  ELECTRICAL 

city  of  the  current  sheet  must  therefore  be  greater 
than  the  standard  velocity.  P  U  measures  the  rota- 
tional, or  magnetic,  energy  of  the  vortex. 

I~P 
The  formula  V  =  ^1        is    an   important   one    in   our 

theory.  It  is  the  velocity  with  which  longitudinal  waves 
of  small  amplitude  are  propagated,  as  well  as  that  of 
electro-magnetic  waves.  However,  vortices  without  vacua 
may  move  rather  slowly.  There  is  a  position  of  equil- 
ibrium where  for  low-rotational  vortices  the  differential 
external  pressure  balances  the  interior  expansional  pres- 
sure. A  vortex  generated  about  a  wire  carrying  a  current 
may  move  out  comparatively  slowly,  and  the  lower  limit 
of  such  a  velocity  is  evidently  zero,  or  a  vortex  may  be 
generated  in  a  position  of  equilibrium. 

When  the  vortices  are  generated  under  a  moderate 
pressure  which  rises  with  no  great  suddenness,  the  rotational 
energies  will  be  low — far  under  the  vacuum  point — and 
the  rings  proceed  to  their  position  of  equilibrium  which 
they  maintain  when  the  current  becomes  steady.  The 
position  of  equilibrium  is  not  now  the  one  we  have  pointed 
out  for  a  single  filament,  but,  since  vortex  lines  when 
pressed  together  exert  a  lateral  pressure  on  each  other, 
the  figure  of  equilibrium  will  be  the  resultant  of  all  these 
lateral  pressures.  It  is  evident  that  when  such  a  tube 
becomes  compressed  the  centrifugal  force  increases,  since 
the  moment  of  momentum  of  the  current  sheet,  or  mrz<*), 
must  remain  constant. 

Let  us  suppose  that  we  have  applied  an  electro-motive 
force  to  a  conductor — say  a  charge  of  positive  electricity, 
or  condensed  ether,  has  been  applied  to  one  end,  and  a 
charge  of  negative  electricity,  or  expanded  ether,  to  the 
other  end,  thereby  establishing  a  pressure  gradient.  An 
equilibrium  of  pressure  is  quickly  established.  In  a 
certain  metaphysical  sense,  it  might  be  considered  that 


MECHANICS  33 

not  only  has  positive  electricity  flowed  in  one  direction 
but  negative  electricity  has  also  flowed  in  the  opposite 
direction,  and  such  is  still  the  general  conception,  although 
the  convention  has  been  made  that  the  direction  in  which 
the  positive  electricity  flows  shall  be  considered  the  direc- 
tion of  the  current.  Actually,  however,  no  negative 
electricity  flows  here,  any  more  than,  when  we  compress 
a  gas  in  one  globe  and  exhaust  it  in  another,  and  connect 
them,  the  rarefied  gas  flows  into  the  compressed  gas. 
The  simple  unquestionable  fact  is  that  condensed  ether 
has  expanded  into  rarefied  ether — positive  into  negative. 
In  nature  motion  can  only  take  place  in  the  direction  of 
a  force,  not  against  it. 

We  have  started  our  current,  but  it  does  not  reach  its 
full  strength  at  once.  It  is  delayed  for  a  time  while  it  is 
building  up  its  system  of  concentric  vortices  surrounding 
the  conductor.  As  layer  after  layer  of  the  rings  are  being 
shot  out,  and  succeeding  layers  are  being  sub-posed,  the 
pressure,  or  electro-motive  force,  is  doing  considerable 
work,  both  in  manufacturing  the  partial  vacua  and  in 
pushing  them  away  from  the  wire.  It  consequently  can 
expend  only  a  part  of  its  energy  in  propelling  the  current 
against  the  resistance  offered  by  the  atomic  surfaces. 

The  field  of  vortex  lines,  or  the  magnetic  field,  throws 
the  medium  surrounding  the  wire  into  a  state  of  strain. 
There  is  a  force  pressing  radially  from  all  directions  upon 
the  wire,  which  is  balanced  by  the  pressure  of  the  current. 
There  is  also  a  pressure  along  the  vortex  filaments  and 
they  behave  as  if  they  were  tense  strings,  always  striving 
to  shorten  themselves.  We  have  already  pointed  out  how 
it  is  possible  for  a  fluid,  isotropic  medium  to  be  put  under 
strains  in  particular  directions  by  motion. 

The  current  finally  becomes  steady.  There  is  now  a 
condition  of  equilibrium  and  the  rings  remain  stationary. 
The  driving  force  is  exactly  balanced  by  the  resistance,  or 
counterpressure,  as  stated  in  Ohm's  law.  But  if  the  cur- 


34  ELECTRICAL 

rent  again  increases,  the  whole  system  moves  outward 
again,  and  a  new  set  of  rings  is  shoved  under  them,  until 
a  new  condition  of  equilibrium  is  established.  If  the 
current  decreases,  the  ring  system  falls  back  towards  the 
wire,  and  the  innermost  are  absorbed  again  into  the 
current  from  which  they  sprang. 

The  vortex  filaments  are  lines  of  magnetic  force.  Every 
current  must  be  accompanied  by  a  magnetic  field*,  and 
the  currents  represented  by  the  current  sheets  have  their 
magnetic  field  wholly  internal.  The  direction  of  the 
magnetic  force  (or  line)  is  perpendicular  to  the  direction 
of  the  current  and  this  condition  must  necessarily  exist 
under  all  circumstances.  If  we  twist  a  wire  into  a  spiral 
coil  and  send  a  current  through  it,  the  circular  lines  of 
magnetic  force  which  surround  a  straight  wire,  will,  in 
this  case,  become  merged  into  a  system  of  closed  lines 
threading  the  coil  through  its  interior,  and  the  direction 
of  rotation  in  the  vortices  will  depend  upon  the  direction 
of  the  current.  The  magnetic  lines  and  current  direction 
are  perpendicular  to  each  other,  as  always. 

Let  us  suppose  a  vortex  ring  just  touching  the  wire 
with  its  inner  edge.  It  is  pressing  upon  the  wire  with  a 
certain  force,  but  this  pressure  is  exactly  balanced  by  the 
pressure  of  the  ether  in  the  current  and  the  ring  conse- 
quently cannot  contract.  But  if  the  pressure  in  the  cur- 
rent falls,  the  ring  begins  to  contract  into  the  wire.  But 
instead  of  doing  this,  it  rolls  itself  out  into  a  linear  current 
on  the  surface  of  the  wire  in  the  direction  of  the  original 
current. 

This  falling  back  of  the  vortices  upon  the  wire  when 
the  current  decreases,  or  is  broken,  is  called  self-induction, 
or  the  "extra  current  on  break."  It  has  been  supposed 
that  it  was  due  to  the  inertia  of  electricity.  Undoubtedly 
the  ether  has  inertia,  but  it  is  very  slight.  Practically  all 
of  the  extra  current  is  due  to  the  discharge  of  the  energy 

*  Linear  currents  in  the  free  ether  are  the  sole  exception. 


MECHANICS  35 

stored  up  in  the  magnetic  field  surrounding  the  wire. 
The  building  up  of  this  field  takes  some  time,  compara- 
tively speaking,  while  its  collapse  on  breaking  the  current 
(or  wire)  is  sudden,  though  not  instantaneous.  No  action 
in  nature  can  take  place  instantaneously,  although  it  has 
been  the  custom  to  consider  gravitation  an  instantaneous 
action. 

The  vortex  lines  which  are  thrown  off  by  a  current 
under  moderate  pressure  and  formed  with  no  great  sud- 
denness, have,  as  we  have  seen,  only  partial  vacua,  and  do 
not  go  to  great  distances  from  the  wire,  even  theoretically. 
They  do  not  extend  indefinitely  into  space,  but  remain 
rather  close,  and  when  the  current  ceases,  all  of  the 
energy,  which  has  been  thus  stored  up  in  the  neighborhood 
of  the  conductor,  is  recovered.  Not  so,  however,  the 
violently  formed  vortices  having  complete  vacua,  which 
constitute  electro-magnetic  waves.  The  energy  in  this 
case  is  thrown  out  into  space  and  permanently  lost. 

Let  us  return  to  the  case  of  a  wire  in  which  a  current 
is  just  starting.  Let  us  suppose  a  second  wire,  parallel 
to  the  first  and  near  it.  During  the  formative  period  of 
the  current,  while  the  circular  vortices  are  being  shot  out, 
these  rings  must  cut  the  second  wire  on  their  out- 
ward journey.  The  filament,  on 
meeting  the  wire,  wraps  itself 
around  it,  reunites  its  ends  on 
the  other  side,  and  continues 
on  as  a  straight  filament.  This 
is  indicated  in  Fig.  3.  For  an 

instant,  a  vortex  ring  surrounds  the  wire,  but,  as  we  have 
seen,  this  instantly  rolls  itself  out  into  a  linear  current 
in  the  second  wire,  having  a  direction  opposite  to  that 
in  the  primary  wire.  The  direction  of  an  induced 
current  is,  of  course,  determined  by  the  direction  of  the 
current  sheet  at  the  point  where  it  first  touches  the  wire. 
When  the  current  in  the  primary  becomes  steady,  its  ring 


36  ELECTRICAL 

vortices  become  stationary,  and  the  induced  currents  in 
the  secondary  wire  cease.  If  the  current  in  the  primary 
now  decreases  or  is  broken,  the  vortex  field  falls  back 
towards  the  primary,  and  such  rings  as  are  outside  the 
secondary  must  cut  it  on  their  return  journey.  In  this 
case  the  inner  edges  of  the  vortices  touch  the  second- 
ary first,  and  the  rotation  is  such  as  to  shoot  the  induced 
current  in  a  forward  direction.  During  the  outward  ex- 
cursion the  ring  system  cuts  the  secondary  wire  more 
slowly,  while  the  inward  fall  is  of  the  nature  of  a 
collapse,  or  a  greater  number  of  lines  cut  the  wire  in  the 
same  interval  of  time.  The  electro-motive  force  of  the 
induced  current  comes  from  the  rotational  energy  of  the 
vortex  filaments.  The  total  number  of  lines  cutting  the 
wire,  outward  and  back,  is,  of  course,  the  same,  and  the 
same  amount  of  electricity  flows  in  the  reverse  and  direct 
induced  currents.  The  direct  induced  current,  however, 
is  under  a  higher  pressure,  and  lasts  a  shorter  time. 

The  motion  between  the  filament  and  the  secondary 
wire,  need,  of  course,  only  be  relative.  Thus  if  the  vortex 
field  is  stationary,  and  the  wire  moves  through  it,  the 
induction  effects  will  be  the  same.  Referring  to  Fig.  3, 
if  a  magnetic  line  is  just  above  the  wire  and  we  send  a 
current  through  the  wire  in  the  direction  of  the  previous 
induced  current,  the  first  vortex  ring  surrounding  the  wire 
will  break  at  the  top  and  become  continuous  with  the 
magnetic  line,  as  shown  in  the  figure.  At  this  instant 
the  magnetic  line  is  partly  bent  around  the  wire,  and,  since 
such  lines  always  strive  to  preserve  a  minimum  length, 
it  will  straighten  out,  thereby  pressing  together  the  lines 
below  and  separating  those  above.  The  lateral  pressure 
will  move  the  wire  upward.  The  direct  pressure  of  the 
vortex  surfaces  on  the  wire  is  resisted  by  the  pressure  of  the 
current  in  the  wire.  The  vortex  cannot  enter  the  wire, 
and  the  latter  is  forced  directly  upward.  Only  a  single 
layer  of  vortices  covers  the  wire  at  any  instant.  The 


MECHANICS  37 

magnetic  lines  above  get  below  the  wire  by  this  process 
of  merging  with  the  surface  (current)  vortices,  and  then 
straighten  out  below. 

If  we  move  the  wire  downward,  a  current  is  induced  in 
the  wire.  If  we  send  an  equal  current  in  the  same  direc- 
tion, the  wire  is  moved  upward,  and  we  shall  have  to  use 
the  same  force  in  moving  the  wire  downward  as  that  with 
which  it  reacts  upward. 

If  we  surround  the  primary  wire  with  a  metallic  cylinder, 
then  every  vortex  travelling  outward  will,  on  striking  its 
inner  surface,  unroll  itself  completely  into  a  linear  current 
travelling  backward.  The  entire  vortex  will  thus  have 
disappeared.  As  no  vortex  can  escape  outside  the  cylinder, 
there  will  be  no  magnetic  field  external  to  it.  On  breaking 
the  primary  current,  only  those  lines  which  are  between 
the  wire  and  the  cylinder  are  left  to  collapse.  Conse- 
quently the  "extra"  current  in  the  primary  will  be  reduced 
by  the  amount  of  the  lines  which  have  been  lost  in  the 
cylinder,  and  there  will  be  no  direct  induced  current  in  the 
secondary.  This  shows  that  electro-magnetic  waves  cannot 
penetrate  a  conductor.  The  reverse  induced  current  on 
the  inner  surface  of  the  cylinder,  however,  sends  out  a 
vortical  system  of  its  own,  and  the  electro-magnetic  waves 
which  left  the  primary  are  thus  reflected  from  the  secondary. 
A  conductor  is  therefore  impermeable  to  electro-magnetic 
waves,  but  it  reflects  them.  This  is  precisely  what  takes 
place  at  the  reflecting  surface  of  an  ordinary  mirror. 
Light,  which  consists  of  electro-magnetic  waves,  cannot 
penetrate  the  surface  of  the  quicksilver,  but  is  reflected. 
The  energy  of  the  reflected  wave  can  never  equal  the  energy 
of  the  original  wave,  since  a  portion  of  this  energy  is  used 
up  in  driving  the  currents  induced  in  the  conductor. 
Hence  conductors  are  opaque  to  electro-magnetic  waves, 
while  non-conductors  transmit  them  and  are  therefore 
transparent.  This  latter  statement  must  be  modified  to 
the  following  extent.  While  all  non-conductors  are  trans- 


38 


ELECTRICAL 


parent  to  electro-magnetic  waves  of  sufficient  length,  yet 
when  these  waves  become  exceedingly  short  and  the 
molecules  of  a  body  are  comparatively  large,  so  that  waves 
and  molecules  are  not  so  greatly  apart  in  the  order  of 
magnitudes,  currents  are  generated  inductively  in  the 
molecules  which  send  back  waves  of  the  same  length  as 
the  impinging  wave.  The  induced  currents  are  thus 
able  to  resonate  with  the  frequency  of  the  impinging  wave 
more  or  less,  with  the  result  that  the  energy  of  the  wave  is 
used  up  in  a  comparatively  short  thickness  of  the  di- 
electric. In  such  a  case  little  of  the  energy  gets  through, 
and  a  small  portion  is  reflected.  Owing  to  this  molecular 
inductive  action,  a  portion  of  very  short  electro-magnetic 
waves  is  always  reflected,  even  in  the  most  transparent 
media.  Thus  glass,  which  easily  transmits  light,  neverthe- 
less reflects  a  small  portion  of  it. 


0 


L 


0000 


B 


Let  us  suppose  that  a  vertical  wire,  AB,  is  traversed  by 
alternating  currents.  A  series  of  vortex  rings  will  be  driven 
out,  one  set  of  them  rotating  one  way,  the  next  set  rotating 
in  the  opposite  direction.  Fig.  4  represents  a  section 
through  the  wire  showing  three  trains  of  vortices,  C,  D,  E, 
consisting  of  four  vortices  in  each  train.  C  rotates  to  the 
right,  D  to  the  left,  and  E  to  the  right  again.  We  shall 
suppose  the  alternations  to  be  very  rapid — some  millions 


MECHANICS  39 

in  a  second.  Of  course,  it  is  possible  to  detect  the  mere 
passage  of  such  a  train  of  electro-magnetic  waves,  and 
signals  could  be  given  by  sending  out  such  a  train,  then 
stopping,  and  then  sending  again.  And  in  fact  this  is 
done  in  wireless  telegraphy.  The  dot  and  dash  messages 
of  the  wireless  codes  are  signaled  by  sending  short  trains 
and  long  trains  with  stops  in  between.  But  it  has  not 
yet  been  possible  to  construct  an  instrument  which  could 
distinguish  between  the  alternations  in  a  continuous  train. 

Let  us  suppose  such  trains  of  vortices  striking  at  some 
distant  point  upon  an  instrument  capable  in  some  way  of 
distinguishing  between  the  alternations.  Let  us  examine 
in  what  way  the  differentiation  of  such  whirls  could  pos- 
sibly be  effected.  Considering  a  single  vortex,  it  would 
appear  that,  since  the  upper  and  lower  edges  arrive  simul- 
taneously at  any  point,  and  are  moving  in  opposite  di- 
rections, any  effect  which  these  motions  might  separately 
produce,  would  certainly  nullify  each  other.  And  con- 
sidering the  front  and  back  edges,  since  the  contiguous 
edges  of  the  neighboring  vortices  move  in  opposite  di- 
rections and  are  in  close  juxtaposition,  thus  arriving  at 
practically  the  same  instant,  it  would  seem  hardly  possible 
that  any  instrument  could  distinguish  between  individuals 
in  a  train  of  vortices  rotating  all  the  same  way.  It  might 
detect  the  front  of  a  train  and  the  rear,  but  during  the 
passage  of  the  train  no  indication  could  be  given. 

However,  at  the  junctions  of  the  oppositely  rotating 
trains,  the  motion  of  the  rear  edge  of  the  last  vortex  co- 
incides with  the  motion  of  the  front  edge  of  the  next  fol- 
lowing vortex.  Hence  at  these  dividing  lines  there  will 
be  a  doubled  upward  motion  followed  by  a  doubled  down- 
ward motion,  and  so  on  alternately.  It  would  seem  pos- 
sible that  such  a  simulated  or  quasi  transverse  vibration 
might  be  detected.  Considering  only  these  up  and  down 
components  of  the  motion,  which  are  the  only  ones  that 
could  possibly  be  detected,  it  is  evident  that  they  would 


40  ELECTRICAL 

form  a  curve  like  that  represented  under  the  trains  C,  D, 
E. 

Let  us  suppose  that  we  make  out  alternations  still 
more  rapid — billions  of  them  in  a  second.  It  is  impossible 
to  get  such  frequencies  in  conductors,  or  oscillators  of 
finite  dimensions,  but  using  an  atom  as  an  oscillator  or 
by  making  an  atom  vibrate  backward  and  forward,  it 
is  possible  to  obtain  such  frequencies,  and  the  vortex 
trains  sent  out  by  such  an  alternating  current  would  be 
reversed  with  this  order  of  frequency.  Such  vibrations 
would  be  something  like  5  X 10 14  times  a  second,  or  the 
same  as  the  frequency  of  light  vibrations.  These  vortices 
are  shot  out  with  a  velocity  of  3  X 10 10  centimetres  per 
second,  which  is  the  velocity  of  light,  and  all  electro- 
magnetic waves  An  atom  vibrating  with  such  fre- 
quencies sends  out  trains  in  which  every  vortex  is  pre- 
ceded and  followed  by  one  rotating  in  an  opposite  di- 
rection, or  every  train  of  the  same  kind  consists  of  only 
one  vortex.  This  is  represented  in  F,  Fig.  4. 

Taking  account  only  of  the  up  and  down  motions, 
which  are  the  only  components  of  the  vortical  motion 
which  could  possibly  be  detected,  we  see  that  this  motion 
is  represented  by  the  curve  under  F.  It  is  a  simple  sine 
wave,  a  complete  wave  length  being  equal  to  two  vortex 
diameters.  We  pointed  out  that  the  only  hope  of  de- 
tecting such  alternating  trains  was  that  there  might  be 
some  instrument  capable  of  being  affected  by  the  up  and 
down,  or  transverse  components  of  the  motion,  which, 
though  acting  in  opposite  directions,  nevertheless  do  not 
act  together  at  the  same  instant  but  are  separated  by  a 
minute  interval  of  time.  Now  there  is  such  an  instrument, 
and  it  is  competent  to  detect  the  transverse  components 
of  electro-magnetic  waves,  provided  the  alternations  are 
of  the  requisite  frequency.  This  instrument  is  the  eye. 

It  has  previously  been  supposed  that,  in  transmitting 
light  waves,  the  motion  of  the  ether  was  purely  trans- 


MECHANICS  41 

versal.  But  it  is  impossible  for  a  fluid  medium  to  execute 
such  motions,  and  it  cannot  transmit  waves  with  trans- 
verse vibrations.  This  is  a  property  of  solids  alone  which 
are  capable  of  undergoing  shearing  strains.  Hence  the 
many  incongruous  and  impossible  descriptions  of  the 
ether.  It  was  said  to  be  a  fluid  with  the  properties  of  a 
solid,  a  jelly,  a  "kind  of  glorified  pitch,"  and  what  not. 
Of  course  nobody  ever  understood  these  descriptions, 
and  especially  not  the  learned  expounders  themselves. 
It  has  done  harm  to  many,  in  that  they  have  been  led  to 
pretend  to  understand  what  was  impossible  of  compre- 
hension, and  it  has  outraged  reason  which  should  be  kept 
sacred. 

We  have  stated  that  electricity  is  the  ether  and  the 
ether  is  electricity — they  are  synonymous.  To  any  one 
who  is  not  convinced  after  reading  the  foregoing  pages, 
the  argument  may  be  put  in  a  more  formal  way.  We 
saw  that  we  were  able  to  produce  a  current  in  a  conductor 
by  simply  touching  a  vortex  filament,  or  line  of  magnetic 
force.  The  question  arises  "Where  did  the  electricity  in  the 
the  conductor  come  from?"  Electricity  is  a  material 
substance  of  some  kind — it  is  something.  Now  anything 
that  exists,  that  is  material,  cannot  be  manufactured  from 
nothing,  neither  can  it  be  destroyed.  The  electricity 
which  we  have  brought  into  the  conductor  must  have 
existed  somewhere  else  before.  It  did  not  exist  in  the 
conductor,  for  a  careful  examination  showed  not  a  trace 
of  electricity  on  it  or  in  it.  It  did  exist  then,  in  the 
magnetic  line.  But  a  magnetic  line  is  simply  ether  in 
motion.  This  can  be  easily  proved,  and  in  fact  nobody 
doubts  it,  although  it  has  not  heretofore  been  recognized 
that  a  magnetic  line  is  simply  a  vortex  filament.  Con- 
sequently electricity  can  be  nothing  else  than  the  ether. 
The  present  mathematical  investigation  showing  that 
such  an  assumption  leads  necessarily  to  all  the  observed 
phenomena,  and  conversely  that  such  phenomena  can  only 


42  ELECTRICAL 

be  produced  by  such  a  mechanism,  lends  cumulative  evi- 
dence that  is  irresistable. 

Certain  metals — iron,  nickel  and  cobalt — possess  a 
curious  property  in  that  their  molecules  are  capable  of 
being  set  in  rotation  about  an  axis  and  of  continuing  this 
rotation  indefinitely.  If  we  place  such  a  body  in  a  mag- 
netic field,  the  axes  of  these  molecules  are  dragged  into 
the  magnetic  lines  and  begin  rotating  with  the  velocity  of 
the  vortex.  They  reinforce  thus  greatly  the  whirl  and 
are  said  to  have  a  very  high  "permeability"  for  magnetic 
lines.  The  theory  of  Ampere  was  that  in  a  magnet,  little 
currents  were  continually  circulating  around  its  molecules, 
and  that  the  axes  of  these  currents  were  all  turned  in  the 
same  direction.  It  is  true  that  there  are  currents  circu- 
lating about  the  magnetic  lines,  but  these  currents  are 
not  limited  to  the  molecules,  but  are  continuous  current 
sheets  forming  a  vortex.  Further  the  molecules  are  not 
stationary,  but  are  rotating  with  the  vortex.  By  their 
momentum  they  reinforce  the  whirl  and  keep  up  the  ro- 
tation even  when  the  magnetic  field  is  withdrawn.  We 
might  consider  these  molecules  as  an  assemblage  of  little 
fans,  whirling  the  ether  around  and  along  the  magnetic 
lines.  It  is  clear  why  the  energy  of  the  whirls  is  so  greatly 
increased,  since  on  the  original  magnetic  field,  the  in- 
dependent field  of  the  molecules  is  superposed. 


Fi^.5 

Fig.  5  represents,  on  the  left,  two  magnets  with  opposite 
poles  next  to  each  other.  The  vortices  traverse  both 
magnets  with  the  intervening  air  gap  and  then  close  round 


MECHANICS  43 

on  the  outside.  Where  the  magnets  are  nearest  the 
vortices  are  crowded  together  and  are  of  greater  cross 
section.  When  isolated  the  number  of  lines  in  the  two 
magnets  is  twice  as  great,  but  when  in  this  position,  they 
join  hands,  a  positive  end  grasping  a  negative  end,  and 
though  the  number  of  lines  is  halved,  the  energy  is  greatly 
increased  in  the  air  gap.  The  outer  lines  are  farther 
apart  and  much  more  tenuous.  The  lines  repel  each 
other  laterally  with  considerable  force  (centrifugal),  but 
are  pressed  together  by  the  general  etheric  pressure,  thus 
assuming  a  pattern  of  equilibrium.  They  always  tend  to 
shorten  and  it  is  evident  that  the  attraction  which  the 
two  magnets  exert  on  each  other  is  due  to  their  being 
pressed  together  by  the  general  etheric  pressure.  In  the 
right  hand  of  Fig.  5  are  two  magnets  with  similar  poles 
opposed.  Similar  lines  do  not  join  hands,  since  if  two 
such  lines  met  head  on,  they  would  be  rotating  in  opposite 
directions.  They  turn  away  and  are  crowded  back,  since 
all  such  lines  repel  each  other  laterally.  This  results  in 
an  elastic  distortion  of  the  original  patterns,  and  since 
these  patterns  always  strive  to  regain  their  original 
symmetrical  shape,  the  magnets  are  pressed  apart. 

The  attraction  is  due  to  the  general  etheric  pressure 
striving  to  close  up  the  partial  vacua  in  the  tubes,  while 
the  repulsion  is  due  to  the  lateral  repulsion  of  the  lines 
striving  to  overcome  the  distortion  of  their  original 
patterns. 


STATIC   ELECTRICITY 


Ether  is  a  condensed  state — of  higher  density  than 
the  normal  ether — is  a  differentiated  condition  which  we 
call  positive  ether  or  positive  electricity.  Likewise  ether 
in  a  rarefied  condition  is  negative  ether  or  negative  elec- 
tricity. While  ether  in  motion  constitutes  an  electric 
current,  if  that  be  not  a  tautological  statement,  positive 
and  negative  ether  at  rest  are  what  is  known  as  static 
electricity. 

We  have  seen  that  gross  matter  at  the  surfaces  of 
solids  and  liquids  is  in  a  differentiated  condition.  The 
molecules  here  are  crowded  together  and  the  matter  is 
much  denser  than  in  the  interior.  The  surface  is  in  a 
state  of  strain,  having  a  "surface  tension," — a  condition 
which  gradually  falls  off  towards  the  interior.  We  have 
also  seen  that  gross  matter  exerts  an  attraction  or  re- 
pulsion on  all  other  matter,  according  as  that  matter  is 
denser  or  less  dense  than  the  ether.  This  action  is  es- 
pecially strong  at  infinitesimal,  or  small,  distances,  rapidly 
falling  off,  so  that  at  a  very  small  distance  from  a  molecule 
it  is  practically  negligible.  A  charge  of  condensed  ether 
will  therefore  be  attracted  and  held  by  a  material  surface, 
while  a  charge  of  negative  ether  will  be  repelled  from 
such  a  surface.  In  the  interior  of  a  conductor,  since  such 
actions  are  from  all  directions,  the  ether  cannot  remain 
in  a  state  of  strain,  but  must  be  at  the  normal  density 
throughout.  A  charge  of  positive  or  negative  ether 
placed  at  some  point  in  the  interior  of  a  conductor  would 
therefore  move  to  the  surface,  where  it  would  be  held. 
Even  if  it  were  on  a  surface  presenting  a  concavity,  it 

44 


MECHANICS  45 

would  represent  here  a  surface  tension  T,  which,  by 
Laplace's  formula,  would  give  rise  to  a  normal  pressure, 

Pn  =  — ,  where  R  is  the  radius  of  curvature  of  the  surface. 
jR 

Since  this  normal  pressure  is  directed  towards  the  interior, 
the  charge  could  not  maintain  its  position,  but  would 
move  through  the  conductor  to  the  convex  side  to  a 
position  of  equilibrium,  where  the  normal  pressures, 
directed  outward,  would  be  balanced  by  the  equal  and 
opposite  attractions  of  the  surface. 

We  shall  assume  that  in  a  conductor  the  atoms  have 
contact  with  each  other  at  some  point,  so  that  a  contin- 
uous surface  is  furnished  over  which  the  charge  can  move. 
In  a  non-conductor,  the  atoms  (molecules)  not  being  in 
contact,  charges  may  be  held  by  each  molecule,  since  this 
ether  is  not  able  to  move  away,  and  may  be  held  locally 
in  a  state  of  strain. 

A  positive  charge  on  a  surface  is  held  by  the  attraction 
of  the  surface  acting  on  the  denser  ether.  Now  this 
attraction  is  proportional  to  the  density  of  the  ether, 
and  since  all  the  layers  apply  their  "weight"  cumulatively 
to  all  the  under  layers,  the  lower-most  layers  will  be  denser 
and  more  strongly  attracted.  We  can  consider  the  sur- 
face to  be  covered  by  an  atmosphere  of  dense  ether  which 
decreases  in  density  progressively  upward,  until  at  a 
certain  short  limit,  which  is  the  height  of  the  atmosphere, 
the  pressure,  or  density,  becomes  equal  to  the  normal 
pressure  of  the  ether.  The  case  is  analogous  to  the 
atmosphere  of  the  earth,  which  decreases  in  density 
logarithmically  upward,  until  it  acquires  the  density  of  the 
ether.  (See  "The  Atmosphere,"  by  the  author.) 

When  a  negative  charge  is  applied  to  a  surface,  the 
gross  matter  repels  it,  and  its  density  increases  upward, 
until  at  a  short  distance — the  height  of  the  charge  at- 
mosphere— the  density  becomes  equal  to  the  normal 


46  ELECTRICAL 

ether  density.  The  previous  case  is  reversed,  and  we 
have  an  inverted  atmosphere.  The  analogous  condition 
for  the  earth  would  be  that  it  were  imbedded  in  an  infinite 
ocean  of  air  having  the  present  density  at  the  surface, 
and  that  the  earth  should  repel  the  air.  In  this  case,  the 
earth  would  have  an  inverted  atmosphere.  For  both 
positive  and  negative  charges,  we  shall  consider  the 
pressure  (density)  at  the  surface,  as  the  pressure,  or 
potential,  of  the  charge.  Actually,  every  charge  contains 
all  pressures  in  its  atmosphere  from  the  normal  ether 
pressure  up  to  (or  down  to)  the  maximum  (or  minimum) 
pressure  of  the  charge. 

If  we  continue  to  introduce  new  masses  of  ether  below 
the  superincumbent  layers,  we  shall  have  to  do  work. 
We  may  do  this  work  by  forcing  ether  onto  the  surface 
against  the  maximum  pressure,  or  we  may  condense  the 
ether  first  and  then  transfer  it  to  the  surface.  As  we  con- 
tinue to  add  thus  new  masses  (charges)  of  ether,  the  pres- 
sure (tension)  of  the  lowest  layer  will  continue  to  rise. 
This  cannot  go  on  indefinitely,  since  the  pressure  of  the 
lowest  layer  will  finally  reach  a  point  where  it  is  equal  to 
the  attracting  or  holding  force  of  the  surface  matter. 
When  this  happens  the  lowest  layer  bursts  or  breaks  away, 
leaving  the  surface  bare  of  any  charge.  From  Laplace's 

formula,  Pn  =  — ,  it  is  evident  that  the  bursting  pressure 
R 

will  be  reached  at  a  very  low  point  on  a  sharply  convex 
surface,  where  the  radius  of  curvature  is  small. 

In  the  same  way,  if  we  keep  introducing  negative  ether 
onto  the  surface,  below  the  other  layers,  a  point  will  be 
reached  where  the  repulsion  will  be  unable  to  withstand 
the  increasing  external  pressure,  and  the  system  will 
break  down.  Since  the  outer  normal  ether  pressure  acts 
with  (in  the  same  direction  as)  the  attraction  on  a  positive 
charge,  and  against  the  repulsion  on  a  negative  charge, 


MECHANICS  47 

it  is  evident  that  a  considerably  higher  pressure  can  be 
reached  in  the  layer  next  to  the  surface  in  a  positive 
charge,  than  the  corresponding  negative  pressure  in  a 
negative  charge.  Or  the  breaking  negative  pressure  of 
a  negative  charge  is  considerably  below  the  corresponding 
positive  pressure  for  a  positive  charge.  It  has  long  been 
known  that  a  negative  charge  breaks  down  under  a  less 
pressure  than  a  positive  charge.  For  a  similar  reason  a 
negative  charge  is  dissipated  more  quickly  than  a  positive 
charge  of  the  same  potential. 

Let  us  suppose  a  spherical  conductor  with  a  positive 
charge,  surrounded  by  a  concentric  metal  spherical  shell, 
with  a  non-conducting  space  separating  them.  The 
longitudinal  positive  waves  given  off  by  the  surface  of  the 
conductor  cause  the  successive  layers  of  the  charge  to 
pulsate.  We  may  consider  these  layers  to  pulsate  syn- 
chronously. The  influence  of  the  charge  may  be  to 
polarize  the  vibrations  of  the  surface  molecules,  so  that 
they  all  vibrate  in  the  same  direction  and  synchronously. 
As  the  compressed  halves  of  the  longitudinal  waves 
emerge  from  the  denser  medium  of  the  charge  into  the 
free  ether,  they  become  transformed  into  expansional 
halves,  and  vice  versa,  the  expansional  halves  of  the 
original  waves,  on  emerging  into  the  free  ether  become 
transformed  into  compressional  halves.  The  character  of 
the  waves  after  passing  through  the  charge  therefore 
becomes  reversed,  and  the  charge  radiates  from  its  surface 
negative  waves.  Or,  considering  a  positive  charge  to  be 
contracting  and  expanding,  it  is  evident  that  the  con- 
traction, or  backward  movement,  must  result  in  increased 
condensation,  while  the  expansion,  or  forward  movement, 
must  result  in  a  rarefaction.  It  is  inevitable,  therefore, 
that  the  waves  emanating  from  its  surface  must  have  their 
condensed  halves  moving  towards  the  disturbing  source, 
and  their  expanded  halves  moving  away  from  it.  The 
reverse  is  the  case  for  negative  charges.  Hence  positive 


48  ELECTRICAL 

charges   radiate   negative   waves   and   negative   charges 
radiate  positive  waves. 

Now  as  the  waves  emanating  from  the  positive  charge 
strike  the  inner  surface  of  the  enveloping  shell,  they  apply 
to  it  in  quick  succession,  positive  and  negative  charges, 
viz.,  their  condensed  and  expanded  portions.  If  the 
central  positive  charge  were  removed,  and  we  should  apply 
successively  positive  and  negative  charges  to  the  inner 
surface  of  the  shell,  they  would  immediately  flow  to  the 
outer  surface  and  there  neutralize  each  other.  But  with 
the  central  positive  charge  in  position,  the  negative  charges 
are  held  (attracted)  and  cannot  flow  to  the  outer  surface. 
The  result  is  that  as  the  waves  deposit  their  charges,  they 
become  separated,  the  positive  charges  appearing  on  the 
outer  surface  and  the  negative  charges  accumulating  on 
the  inner  surface.  It  may  appear  unintelligible  why  the 
two  charges  do  not  neutralize  each  other  on  the  inner 
surface,  but  experiment  shows  that  if  we  have  a  bound 
(induced)  charge  on  one  side  of  a  conductor  and  no  charge 
on  the  other  side  (removed  by  earthing),  we  can  apply  an 
opposite  charge  to  the  conductor  which  will  reside  on  the 
previously  uncharged  side,  and  it  makes  no  difference  to 
which  side  we  apply  this  charge.  In  the  case  of  our  shell, 
the  explanation  probably  is  that  the  waves  are  simply 
transmitted  through  the  bound  negative  charge  as  through 
a  rarer  medium,  and  appear  intact  on  the  outside. 

We  have  said  that  the  total  energy  of  a  unit  mass  of 
ether  is  proportional  to  its  absolute  pressure.  The  ether, 
therefore,  represents  a  tremendous  amount  of  energy. 
It  conserves  this  energy  from  the  fact  that  its  total  body 
is  at  a  uniform  pressure  and  there  is  no  other  source  of 
higher  or  lower  potential  from  which  it  may  gain  or  lose 
energy.  Where  this  original  energy  came  from,  and  by 
what  mechanism  it  manifests  itself,  i.e.,  by  what  form  of 
motion  its  pressure  is  exercised,  has,  as  yet,  been  the  subject 
of  the  barest  surmise. 


MECHANICS  49 

We  shall  assume  that  the  rate  of  energy  outflow,  or  the 
rate  of  the  dissipation  of  the  energy  of  a  body,  is  pro- 
portional to  its  potential  or  pressure.  Two  bodies  radiate 
their  energy  to  each  other,  but  if  they  are  at  the  same 
potential,  the  gain  is  equal  to  the  loss  and  their  potentials 
remain  unchanged.  A  charge  of  ether,  having  a  greater 
potential  than  the  normal  ether,  must  dissipate  its  energy 
at  a  rate  proportional  to  the  excess  of  its  pressure  above 
that  of  the  general  ether.  Practically  it  is  found  that  a 
charge  of  electricity  is  dissipated  at  a  rate  proportional  to 
its  pressure  above  the  normal,  just  as  a  hot  body  cools  at 
a  rate  proportional  to  its  temperature  above  its  sur- 
roundings (Newton's  law*).  Temperature  is  the  analogue 
of  a  potential  or  it  can  be  considered  a  heat  potential. 
Thus  a  positive  charge  continually  loses  energy,  and  a 
negative  charge  continually  gains  energy.  We  have  every 
reason  to  believe  that  the  energy  of  a  charge  is  dissipated 
through  longitudinal  waves. 

Stephan  has  found  that  for  very  high  temperatures  (such  as 
that  of  the  sun)  the  rate  of  radiation  is  best  represented  by  the 
fourth  power  of  the  absolute  temperature.  We  have  to  do  here 
with  electro- magnetic  waves  (heat),  and  the  ratio  of  the  output  of 
energy  in  unit  time  to  the  potential  of  the  source  does  not  remain 
constant,  as  with  longitudinal  waves,  but  increases  progressively 
as  the  potential  rises. 

The  quantity,  Q,  or  mass  of  ether  in  a  charge  is  pro- 
portional to  its  volume  by  its  pressure,  p,  above  the 
normal.  The  volume  of  the  charge  is  Sh,  where  5  is  its 
surface  and  h  is  the  height  of  the  charge.  Since  h  is  always 
small  and  does  not  vary  appreciably  we  can  assume  the 
volume  to  be  sensibly  proportional  to  the  surface,  and 
therefore  Q  =  pS.  Let  E  be  the  energy  in  a  wave  given 

off  by  unit  surface  of  a  charge.     Then  — ,  where  t  is  the 

time  of  a  complete  wave  vibration,  is  the  output  of  energy 

*  We  exclude,  of  course,  leakage  by  conduction  and  convection. 


50  ELECTRICAL 

per  unit  surface,  per  unit  time.     This  is  proportional  to  the 

pressure,  or  —  =  kp  =  k  —  .     Or  -    -   =  kQ.     Hence  the 

t  o  t 

rate  at  which  the  energy  flows  across  an  enveloping  sur- 
face is  proportional  to  the  charge. 

The  radiations  from  our  three  charges  are  all  directed 
away  from  their  respective  surfaces,  so  that  the  external 
positive  charge  can  in  no  way  influence  the  internal 
charges.  If  a  charge  were  outside  and  wholly  detached, 
it  would  merely  induce  charges  on  the  outer  surface  of 
the  shell  and  therefore  could  in  no  way  influence  the 
internal  charges.  This  is  a  general  principle,  viz.,  that 
no  external  charge  can  in  any  way  influence,  or  exert  a 
force  upon,  an  internal  charge.  But  a  charge  placed  in 
the  interior  of  a  hollow  conductor  can  influence  outside 
charges  through  the  induced  charge  which  appears  on 
the  outer  surface.  We  shall  hereafter  not  consider  this 
external  charge,  as  we  are  to  deal  only  with  the  internal 
charges.  Whether  we  remove  it  by  earthing,  or  not,  will 
make  no  difference. 

We  have  said  that  the  waves  radiated  by  the  central 
charge  apply  successively  positive  and  negative  charges 
to  the  outer  and  inner  surfaces  of  our  shell.  But  this 
cannot  go  on  indefinitely.  When  the  outflow  of  energy 
from  the  inner  charge  is  equal  to  that  which  it  gains  from 
the  central  charge,  its  energy  can  no  longer  increase,  but 
remains  stationary.  Since  the  total  energy  flowing  into 
the  inner  charge  is  proportional  to  Q,  the  central  charge, 
and  the  total  energy  flowing  out  of  the  inner  charge  is 
proportional  to  Q1,  its  own  charge,  when  Q  =  Ql  there 
can  be  no  further  increase,  and  the  induced  charges  on 
the  shell  become,  practically  instantaneously,  equal  to  the 
central  charge,  and  remain  so. 

We  have  seen  that  the  attraction  of  longitudinal  waves 
on  a  body  having  a  density  different  from  that  of  the  ether 


MECHANICS  51 


£     £)1 £) 

is  — . S,    where  E  is   the   energy  in  a  unit  cross 

section  of  the  wave,  and  Dlt  and  5,  are  the  density  and 
surface  respectively  of  the  body  acted  upon.  The  central 
charge  will  therefore  attract  the  inner  charge  with  a  force 

proportional  to — -1. — 52,  where  Si,  is  the  surface 

of  the  central  charge,  and  S2  and  D2,  the  surface  and  den- 
sity of  the  inner  charge.  But  we  have  seen  that  we  can 

write  -  -  =  Q,  and  since  the  density  of  a  charge  is  pro- 
portional to  its  absolute  pressure  above  zero,  we  can 

p p 

write   the    attractional   force,  Q.—       —  S2.     Calling   pi, 

Pz 

and   p2,   the   pressures   of   the   two   charges   above   and 

below  the   normal    pressure,  this   becomes   Q^— — -.     But 

P2 

pzSz  =  Q,  and  the  attractive  force  is  proportional  to 
— .  Likewise  we  find  that  the  attraction  of  the  inner 

QZ  p p 

charge  is  — .     Now  the  fraction   — is  sensibly  the 

PI                                               PI 
p  p  /p  P\2 

same  as  — ,    since  they  differ  only  by  — — ,  and 

P  P\P 

(Pi — P)2  is  very  small  and  PXP  is  relatively  very 
large.  Hence,  although  the  attraction  of  the  central 
charge  on  the  inner  charge  is  very  slightly  greater  than 
vice  versa,  yet  they  are  sensibly  equal,  and  the  mutual 
attraction  is  proportional  to  Q2. 

If  two  charges  are  on  non-conductors  (such  as  pith 
balls),  where  inductive  action  is  not  possible,  and  one 
body  does  not  surround  the  other,  but  they  arc  small 


52  ELECTRICAL 

compared  with  their  distance  apart,  the  mutual  attraction 

00 l 

becomes  proportional  to  =~-,  since  the  energy  per  unit 

r2 

surface  falls  off  inversely  as  the  square  of  the  distance. 
This  was  discovered  by  Coulomb  experimentally,  and  is 
known  as  Coulomb's  law. 

If  the  medium  between  the  two  charges  becomes  denser, 
so  that  the  velocity  of  wave  proportion  becomes  less, 
or  t  becomes  greater,  or,  what  is  the  same  thing,  the 
quantity  of  energy  flowing  in  unit  time  becomes  less,  the 
attraction  between  the  charges  becomes  less,  since  the 

£ 
force  is  proportional  to  —  5  .  Q1,  5  being  the  surface  of 

the  radiating  body. 

Two  bodies  charged  with  opposite  charges  of  electricity 
attract  each  other  because  the  charges  exert  attractions 
on  each  other.  The  charges  cannot  leave  the  bodies  since 
they  are  held  by  the  surface  attraction  and  the  bodies  are 
forced  to  follow  the  movements  of  the  charges.  The 
atoms,  of  course,  attract  each  other,  but  since  this  action 
is  upon  discrete  specks  of  surface,  while  that  of  the  charges 
is  upon  large  continuous  surfaces,  the  atomic  attraction 
is  insensible,  while  the  electrical  attraction  is  comparatively 
very  large,  and  very  appreciable. 

Returning  to  our  shell,  let  p  be  the  pressure  which  the 
central  charge  had  before  it  was  introduced  into  the  hollow 
conductor.  Then,  at  that  time,  Q  =  kpS,  or,  for  a  given 
pressure,  the  capacity  was  proportional  to  the  surface,  k 
being  the  proportionality  factor.  Inside  the  conductor, 
the  pressure  becomes  p — Q2,  since  it  is  lessened  by  the 
amount  of  the  mutual  attraction  of  the  charges.  Since  the 
charge  must  remain  the  same,  we  have 

Q  =kpS  =fe'  (p-Q*)  S, 
where   kl  is  a  new   proportionality  factor   of  capacity. 


MECHANICS  53 

_  _  P  The  new  specific  capacity  factor  is,  therefore, 
k  P-Q, 

very  much  greater  than  the  old  one,  or  it  will  be  possible 
to  load  the  same  surface  with  a  much  greater  quantity  of 
electricity  before  reaching  the  same  potential.  Hence,  by 
allowing  the  central  surface  to  be  in  communication  with 
some  source  of  electricity,  kept  at  a  constant  potential, 
it  will  be  possible,  by  the  aid  of  the  attraction  of  the  inner 
induced  charge,  to  load  it  with  an  enormously  greater 
quantity  of  electricity  than  if  it  were  isolated. 

If  we  fill  the  space  between  the  two  charges  with  some 
denser  dielectric,  which  reduces  the  velocity  of  wave 
propagation,  we  shall  get  a  new  factor  of  specific  induction. 
The  mutual  attraction  of  the  two  charges  is  proportional 

0* 

to  ~,  becoming  less  as  tl  becomes  greater.     The  attraction 

exercised  by  a  material  surface  on  a  charge  is  proportional 
to  the  pressure  of  the  charge.  Let  g  be  this  attraction 
per  unit  of  surface.  Then  the  surface  attraction  on  the 

Qt 

charge  will  be  gp,  and  gp  —  —  =  p,    or    Qf  =p(g—  I)*1. 

ti 

If  we  keep  the  central  charge  connected  with  a  source  of 
electricity  at  constant  potential,  p,  the  electricity  flowing 
in  will  increase  the  charge,  but  as  the  quantity  increases, 
the  inner  induced  charge  also  increases,  and  their  mutual 
attraction,  tending  to  lower  the  pressure,  increases  as  the 
square  of  the  quantities.  Q2  is  proportional  to  tl.  Hence 
as  the  velocity  of  wave  propagation  in  the  medium  de- 
creases, the  load  of  electricity  at  a  given  potential  becomes 
greater.  If  we  take  the  ratio  of  the  quantity  of  electricity 
with  which  we  must  load  the  central  conductor  to  bring 
it  up  to  a  certain  potential  when  a  dense  dielectric  is  used, 
to  the  quantity  necessary  to  bring  it  to  the  same  potential 
when  only  ether  intervenes,  we  shall  obtain  the  specific 


54  ELECTRICAL 

inductive  factor  of  the  dielectric.  This  quantity  is 
usually  designated  by  K,  and  is  called  the  specific  in- 
ductive capacity. 

K    =      Ih    =     /Z,   where    t1    and    V1    are    the    time 

of  a  wave  vibration  and  its  velocity  in  the  dielectric, 
and  t  and  V  are  the  corresponding  quantities  in  the 
ether.  K  is  not  constant  for  the  same  dielectric,  but 
varies  with  its  temperature  and  from  other  circum- 
stances which  we  shall  discuss  later.  Assuming  K  to 
be  determined  for  a  given  temperature,  and  in  a  simple 
induction,  i.e.,  one  without  complicating  factors,  the 
attraction  between  two  opposite  charges  would  be  pro- 

00  l 
portional  to  -^  —  ,  and  the  specific  inductive  capacity  of 

the  dielectric  would  be  K  =  _  /JL.     The  mutual  attraction 


between  the  central  and  inner  charges  of  our  shell  varies 

as  JL    or  as  the  velocity  of  wave  propagation  in  the 
K* 

medium  separating  them,  but  if  the  central  charge  be 
kept  in  communication  with  a  source  at  constant  potential, 
the  attraction  will  not  vary,  no  matter  how  the  dielectric 

Q2 

varies,  for  —  =  p  (g  —  1),  which  shows  that  the  attraction 

remains  constant. 

We  have  hitherto  considered  the  action  of  the  dielectric 
as  simply  that  of  transmitting  longitudinal  waves.  But  if 
we  place  a  solid  dielectric  between  the  two  plates  of  a 
condenser  the  molecules  will  become  loaded  individually 
by  induction.  The  waves  will  deposit  positive  charges 
on  one  side  and  equal  negative  charges  on  the  other. 


MECHANICS  55 

They  will  become  polarized  in  the  direction  of  the  waves. 
Now  in  a  single  conductor,  as  soon  as  the  inducing  charge 
is  removed,  the  equal  and  opposite  induced  charges  im- 
mediately reunite,  but  in  a  nonconductor,  the  molecules 
have  their  charges  aligned  so  that  the  molecule  next  ahead 
turns  an  opposite  charge  to  that  on  the  molecule  next 
behind.  These  opposite  charges  attract  and  hold  each 
other,  so  that  when  the  electric  field  is  removed,  the 
charges  do  not  reunite,  but  maintain  their  positions. 
They  are  now  an  independent  source  of  energy  and  send 
out  waves  in  the  direction  in  which  they  are  aligned. 
The  case  is  analogous  to  that  of  a  magnet,  which,  even 
after  the  polarizing  source  is  removed,  maintains  its  in- 
dependent field  in  the  same  direction.  Hence  the  induced 
charges  in  a  condenser,  which,  for  a  given  potential,  are 
greater  as  the  wave  velocity  decreases,  are  still  further 
increased  by  this  action  in  the  dielectric.  The  molecules 
have  stored  up  an  independent  source  of  energy  which  is 
super  added  to  that  of  the  original  field. 

If  we  place  a  plate  of  mica  in  a  strong  electric  field 
(between  the  plates  of  a  condenser),  the  mutual  attraction 
of  the  induced  charges  on  its  molecules  puts  it  in  a  state 
of  strain.  It  is  as  if  the  plate  were  pressed  between  the 
jaws  of  a  vise.  If  the  pressure  becomes  too  great,  some 
of  the  molecules,  along  a  line  of  weakest  resistance  are 
forced  away  from  their  positions  of  equilibrium  and  a 
fracture  results.  If  we  peel  off  leaves  from  the  plate,  we 
shall  find  that  throughout  there  are  always  charges  of  one 
kind  on  one  side  and  charges  of  the  opposite  kind  on  the 
other,  no  matter  how  thin  the  leaves  are.  This  action  is 
not  so  strongly  marked  in  liquids,  and  of  course  when  the 
electric  field  is  removed,  no  polarization  remains.  A  solid 
dielectric  so  internally  polarized  has  been  called  by 
Heaviside  an  Electret,  from  its  analogy  to  a  magnet.  The 
strain  in  a  transparent  dielectric  like  glass  is  easily  demon- 
strated by  a  ray  of  light.  Since  it  is  compressed  in  the 


56  ELECTRICAL 

direction  of  the  field,  it  will  behave  like  a  uniaxial  crystal, 
subjecting  light  to  a  double  refraction,  and  transmitting 
an  ordinary  ray  and  an  extraordinary  ray. 

We  have  seen  that  the  specific  inductive  capacity  of  a 
substance  varies  inversely  as  the  square  root  of  the  velocity 

of  wave  propagation  in  it,  or  K  =  */ — .     This  is  for  a 

simple  inductive  action.  But,  for  solid  and  liquid  di- 
electrics, this  is  complicated  by  the  electret  action,  and 
the  induction  becomes  a  more  complicated  function.  It 
is  further  complicated  by  the  temperature  of  the  substance 
since  the  condition  of  the  molecules  as  to  motion  must 
markedly  affect  all  inductive  action.  It  would  therefore 
be  difficult  to  derive  a  formula  connecting  all  these  vari- 
ables. Even  experimentally  it  is  extremely  difficult  to 
determine  the  inductive  factor  with  reasonable  accuracy. 
Various  investigators  give  rather  different  determinations 
for  various  substances.  Thus  we  have 

FOR  SHELLAC  Faraday  1 . 55 

Thornton  2.49 

Everett  2.00 

FOB  SULPHUR  Thornton  4 . 03 

Ganot  4.73 

Everett  2 . 24 

FOR  RESIN  Thornton  3.09 

Ganot  2.55 

Everett  1.77 

FOR  GLASS  Everett  1 . 75 

Thornton  6  to  10 

V2 
According  to  Maxwell's  theory  K  =  —^  .     This  is  known 

y 

as  Maxwell's  law.  Since  —  is  the  index  of  refraction  of  a 

V1 

substance  for  longitudinal  waves,   K  =  n2,  where  n  is  the 


MECHANICS  57 

index  of  refraction.  We  have  found  that  in  a  simple 
(uncomplicated)  induction,  K  =  V~n.  A  few  substances 
have  been  found  which  conform  to  Maxwell's  law  more  or 
less,  but  *" Exceptions  are  much  more  numerous  than 
accordances."  Likewise  it  is  possible  to  select  a  list 
which  conforms  approximately  to  the  formula  K  =  V~n> 
but  neither  of  these  formulas  represent  all  the  conditions, 
and  neither  can  be  considered  a  law. 

When  two  different  substances  are  rubbed  together, 
the  vibrations  of  the  molecules  on  the  opposing  surfaces 
become  polarized  and  are  directed  across  the  junction. 
Waves  are  set  up,  which  according  to  the  relative  condi- 
tions existing  in  the  two  kinds  of  molecules,  are  in  one 
direction  or  the  other.  Simple  contact  is  sufficient  to 
set  up  such  waves.  Thus  when  zinc  and  copper  are 
brought  together,  positive  waves  flow  across  the  junction 
from  the  zinc  to  the  copper.  These  waves  deposit  charges, 
and  the  wave  force  keeps  the  negative  charges  at  the 
copper  end  and  the  positive  charges  at  the  zinc  end. 
When  glass  and  resin  are  rubbed  together,  the  glass  ac- 
quires a  positive  charge;  the  resin  a  negative  charge.  In 
a  circuit  of  different  metals  such  waves  are  set  up  at  the 
junctions,  but  their  algebraic  sum  is  zero,  and  therefore 
no  current  flows.  However,  if  the  wave  energy  at  one 
junction  is  differentiated  from  the  rest  by  heating  or  cool- 
ing, a  feeble  current  ensues. 

A  charged  spherical  body  sends  out  its  waves  radially. 
A  small  charge  in  its  neighborhood  will  be  attracted  or 
repelled  along  a  radial  line,  if  no  other  charged  body  be 
near.  If  another  charged  body  be  near,  this  likewise  will 
radiate  waves  in  straight  lines  from  its  surface,  the  radia- 
tions from  both  bodies  taking  place  exactly  the  same  as  if 
the  other  were  not  present,  providing  the  charges  are  on 
nonconductors,  and  their  distribution  cannot  be  altered 
inductively. 

*  Ganot's  Physics. 


58  ELECTRICAL 

If  we  explore  the  combined  field  with  a  small  charge, 
it  will  move  in  a  path,  the  direction  of  which  at  any  point, 
is  the  resultant  of  the  forces  arising  from  the  two  inde- 
pendent fields.  If  the  two  bodies  are  oppositely  charged, 
the  path  will  be  a  curved  line  leading  from  a  positive  charge 
on  the  surface  of  one  body  to  an  equal  negative  charge 
on  a  certain  point  of  the  other  body.  We  could  map  out 
the  different  curved  paths  which  such  a  small  charge  would 
follow  starting  from  different  points  of  one  surface,  and 
these  paths  would  represent  the  combined  field  of  force 
between  the  two  bodies.  These  different  paths  are  called 
lines  of  electric  force.  They  have  however  no  actual 
existence,  but  are  merely  mathematical  figments.  What 
actually  exists  are  the  wave  trains  being  given  off  by  each 
charge,  and  these  pursue  their  course  absolutely  unin- 
fluenced by  one  another.  This  is  not  the  case  with  mag- 
netic lines,  which  are  physical  realities — actual  linear 
vortices  in  the  ether — and  the  presence  of  other  lines 
influences  their  condition  greatly,  leading  to  their  merging 
together  or  repelling  each  other. 

The  case  of  a  conductor  offers  a  peculiar  situation  as  regards  the 
specific  inductive  factor,  K.  It  has  been  considered  that  K  for 
a  conductor  must  be  regarded  as  infinite,  in  which  case  the  velocity 
of  wave  propagation  would  be  zero.  This  would  have  to  be  in- 
terpreted that  no  longitudinal  waves  can  exist  in  such  a  medium. 
We  might  perhaps  equally  well  consider  K  here  as  zero,  or  the 
wave  velocity  infinite.  The  fact  appears  to  be  that  there  is  really 
no  such  thing  as  an  inductive  coefficient  for  a  conductor,  and  we 
might  as  well  speak  of  the  temperature  of  a  charge  of  electricity. 

Starting  with  the  hypothesis  that  static  charges  of 
electricity  were  simply  differentiated  portions  of  the  ether, 
denser  or  less  dense  than  the  general  ether;  that  such 
charges  continually  give  off  longitudinal  waves  of  two 
different  kinds,  according  as  they  are  positive  or  negative, 
positive  charges  giving  off  negative  waves  and  negative 
charges  giving  off  positive  waves;  and  that  all  electrical 
actions  at  a  distance  (attractions  and  repulsions)  were 


MECHANICS  59 

due  to  these  waves;  we  have  been  able  to  deduce  theo- 
retically all  known  facts  regarding  electrical  actions. 
The  steps  in  the  reasoning  are 

1.  Action  at  a  distance  can  only  be  effected  through  a 
medium.  2.  That  medium  is  the  ether.  3.  Such 
action  can  only  be  effected  by  some  kind  of  motion  in 
the  medium,  and  this  motion  must  be  imparted  by  the 
acting  body.  A  dead  body  cannot  act,  although  it  may 
be  acted  upon.  So  far  we  are  upon  uncontrovertible 
ground.  4.  Longitudinal  waves  necessarily  cause  such 
actions  (attractions  and  repulsions)  and,  excluding  mag- 
netic actions  which  have  no  place  in  electrical  actions, 
they  are  the  only  kind  of  motion  in  the  medium  capable 
of  effecting  these  actions. 

An  exception  may  be  taken  to  No.  4.  It  may  be  said 
that,  granted  longitudinal  waves  can  produce  such  actions, 
there  may  possibly  be  some  other  kind  of  motion,  which 
we  have  not  thought  of,  capable  of  producing  exactly  the 
same  effects.  The  probability  of  any  other  kind  of 
motion  producing  the  many  diverse  and  complicated 
phenomena  of  electricity;  of  the  exact  agreement  of  all 
its  effects  with  those  of  longitudinal  waves,  though  itself 
different,  is  infinitesimal. 


ELECTRO-CHEMISTRY 


In  Fig.  6  we  have  a  cell  containing   dilute  sulphuric 
acid  in  which  zinc  and  copper  plates  are  immersed.     To 
each  plate  is   connected  a  wire  of   the  same  material. 
When  the  wires  are  not  in  contact 
no  acti°n  °f  any  kind  takes  place, 
but   when  the   wires  touch,  at  the 
H  ?  S  O  4  J  surface  of  contact  longitudinal  waves 

are  set  up,  the  direction  of  which  is 
determined  by  the  nature  of  the  two 
pj  A  5  kinds  of  molecules.     When  zinc  and 

copper  are  in  contact  the  direction 
of  the  waves  is  from  the  zinc  to  the  copper,  so  that  a 
positive  charge  is  produced  and  held  in  the  zinc  end,  while 
a  negative  charge  is  applied  to  and  held  on  the  copper 
plate.  If  the  positive  charge  on  the  zinc  plate  could 
flow  through  the  liquid  to  the  copper  plate,  a  current 
would  flow  and  there  would  be  an  immediate  equalization 
of  potential.  But  the  molecules  of  liquids  are  not  in 
contact  and  a  current,  therefore,  cannot  flow  through 
a  liquid.  They  are  absolute  nonconductors.  Under  an 
enormous  pressure,  a  path  could  be  broken  through  the 
molecules  by  a  charge,  just  as  it  is  possible  to  break  down 
any  dielectric,  but  this  is  not  conduction.  Our  plates 
oppositely  charged  therefore  form  a  condenser,  of  which 
the  liquid  is  the  dielectric.  The  liquid,  in  fact,  becomes 
a  fluid  electret.  It  is  under  a  state  of  strain,  and  its 
molecules  arrange  themselves  with  their  negative  charges 
pointing  towards  the  zinc,  and  their  positive  charges 
pointing  towards  the  copper. 

60 


MECHANICS  61 

Now  the  atoms  of  a  chemical  compound  are  held  to- 
gether as  molecules  by  the  action  of  equal  and  opposite 
charges  on  the  various  atoms.  Thus,  in  HCl,  there  is  a 
positive  charge  on  the  hydrogen  atom,  and  an  equal 
negative  charge  on  the  chlorine  atom.  The  atoms  never 
come  into  actual  contact,  but  are  held  together  by  the 
mutual  attraction  of  their  two  opposite  charges.  It  has 
been  supposed  that  they  revolve  about  their  common 
inertianal  centre,  just  as  two  heavenly  bodies  do,  the  cen- 
trifugal force  balancing  the  attractional  force,  but  this  is 
a  matter  which  does  not  concern  us  here.  The  important 
point  is  that  what  is  known  as  chemical  affinity  between 
atoms  is  due  simply  to  the  attraction  of  equal  and  opposite 
charges  on  the  atoms  or  radicles. 

But  to  return  to  our  liquid  electret.  The  molecule  of 
sulphuric  acid  is  composed  of  two  atoms  of  hydrogen, 
each  with  a  definite  charge  of  positive  electricity,  and  a 
radicle  50  4  which  holds  a  negative  charge  equal  to  the 
positive  charges  on  the  hydrogen  atoms,  or  equal  to  double 
the  charge  on  a  single  hydrogen  atom.  In  the  electric 
field  between  the  two  plates  the  atoms  arrange  themselves 
in  the  direction  of  the  strain  (wave)  lines — the  hydrogen 
atoms  being  nearest  to  the  copper,  and  the  radicle  50  4 
nearest  the  zinc.  The  molecules  of  the  liquid  do  not  come 
into  actual  contact  with  the  plates.  Hence,  in  an  un- 
polarized  condition,  no  charge  exists  on  the  plates  ac- 
quired either  inductively  or  by  direct  application.  But 
in  a  polarized  condition  the  hydrogen  atoms  next  to  the 
copper  plate  all  face  towards  this  plate,  and  the  50  4 
radicles  next  to  the  zinc  plate  all  face  towards  this  plate. 
Extra  charges  are  thus  induced  on  the  two  plates — the 
hydrogen  atoms  inducing  an  equal  charge  of  negative 
electricity  on  the  copper,  while  the  504  radicles  induce  an 
equal  charge  of  positive  electricity  on  the  zinc.  The 
result  is  that  the  molecules  immediately  next  to  the  two 
plates  become  torn  apart,  the  positive  halves  being  urged 


62  ELECTRICAL 

in  one  direction,  while  the  negative  halves  are  urged  in 
the  other.  These  two  oppositely  charged  parts  of  a 
molecule  are  called  ions.  The  negative  ions  (504)  are 
urged  towards  the  zinc,  while  the  positive  ions  (H)  are 
repelled  from  the  zinc  and  urged  towards  the  copper. 
Thus  there  is  a  procession  of  hydrogen  ions  towards  the 
copper,  and  a  procession  of  S04  ions  towards  the  zinc. 
This  is  called  the  "Migration  of  the  ions."  As  soon  as  the 
two  hydrogen  atoms  are  detached  from  the  molecules, 
they  mutually  repel  each  other,  while  the  50 4  radicle 
remains  intact  with  its  double  charge.  This  double 
negative  charge  is  able  to  detach  an  atom  of  zinc  which 
has,  of  course,  an  equal  positive  charge,  and  thus  a  new 
molecule  of  ZnSO<  is  formed.  The  hydrogen  atoms  with 
their  single  charge  are  unable  to  detach  an  atom  of  copper, 
and  being  drawn  into  actual  contact  give  up  their  charges 
to  the  copper.  The  action  may  be  summed  up  as  follows : 
The  hydrogen  atoms  which  previously  held  positive 
charges  and  were  bound  in  an  H2S*0  molecule,  are  now 
isolated  and  without  charge.  The  zinc  atoms  on  the 
surface,  which  previously  held  only  a  weak  charge,  though 
sufficient  to  polarize  the  field,  have  now  acquired  a  strong 
positive  charge,  viz.,  that  of  which  the  hydrogen  atoms 
have  been  deprived,  and  by  virtue  of  the  acquired  charge 
are  now  the  positive  halves  of  a  new  molecule,  Z«S04. 
The  transference  of  the  positive  charges  from  the  hydro- 
gen atoms  to  the  zinc  atoms  has  been  effected  through  the 
connecting  wire.  A  current  has  flowed  from  the  copper  to 
the  zinc.  The  charges  produced  by  the  contact  of  the 
wires  were  weak.  They  play  little  part  in  the  process, 
except  by  setting  up  the  original  field  and  determining 
in  which  direction  the  action  shall  take  place.  The 
principal  part  is  played  by  the  strong  induced  forces. 
The  mutual  attraction  between  the  double  charges  on  the 
S04  radicles  and  the  double  charges  on  the  zinc  atoms, 
which  was  proportional  to  4Q2,  was  sufficient  to  detach 


MECHANICS  63 

the  zinc  atoms,  while  the  mutual  attraction  between  the 
charges  on  the  hydrogen  atoms  and  on  the  copper  atoms, 
which  was  proportional  to  Q2,  was  insufficient  to  detach 
a  copper  atom.  Otherwise  stated,  the  chemical  affinity 
between  Zn  and  S04  is  four  times  greater  than  that 
between  Cu  and  H.  Certain  atoms  are  capable  of  taking 
only  a  single  definite  charge  of  electricity.  Other  atoms 
may  take  double  or  three  times  this  minimum  amount, 
but  it  is  always  an  exact  multiple  of  the  minimum  amount. 
Atoms  taking  only  the  minimum  charge  are  called  univa- 
lent;  atoms  taking  twice  this  amount,  bivalent,  and  so  on. 
This  is  perhaps  because  univalent  atoms  all  have  the  same 
maximum  capacity.  We  may  suppose  atoms  of  a  higher 
valency  to  have  a  greater  maximum  capacity.  Thus  a 
bivalent  atom,  or  one  capable  of  holding  two  univalent 
atoms,  is  able  to  support  two  minimum  charges,  each 
charge  holding  one  of  the  univalent  atoms.  Since  the 
attraction  between  atoms  is  always  inductive,  their 
charges  in  a  molecule  must  be  equal  and  opposite.  In 
every  case  the  algebraic  sum  of  the  charges  in  a  molecule 
must  always  be  zero. 

While  the  univalent  charge  must  be  regarded  as  the 
saturation  charge  for  the  atom,  beyond  which  it  cannot  be 
loaded,  the  charge  on  an  atom  of  higher  valency  may  be 
far  from  the  saturation  point.  Thus  in  HgCl,  Hg  has 
only  the  minimum  charge,  and  is  not  saturated,  for  it 
easily  holds  twice  this  amount  in  the  compound  HgCh. 
In  our  previous  experiment  with  the  galvanic  cell,  in  which 
we  converted  a  molecule  of  J/2504  into  a  molecule  of 
ZnS04  by  transferring  the  positive  charges  on  the  hydrogen 
to  the  zinc  atom,  we  have  done  work.  For  the  current 
which  flowed  in  the  wire  heated  the  wire,  thereby  expending 
energy.  Hence  the  electrical  energy  in  the  ZnS04  mole- 
cule must  be  less  than  that  in  the  H2SOt  molecule.  The 
quantity  of  electricity  is  the  same,  but  the  pressure  must 
be  less.  We  have  seen  that  the  mutual  attraction  of  two 


64  ELECTRICAL 

charges  lowers  their  pressure.  The  attraction  on  the 
hydrogen  charges  lowers  their  pressure  by  an  amount 
proportional  to  2Q2,  while  the  attraction  on  the  zinc 
charge  lowers  its  pressure  by  double  this  amount,  or  pro- 
portionally to  4Q2.  The  charges  on  the  hydrogen  atoms, 
therefore,  have  forced  their  way  through  the  resistance 
of  the  wire  by  sacrificing  a  part  of  their  pressure. 

If  we  place  two  platinum  electrodes  in  a  cell  containing 
H20,  and  give  one  electrode  a  positive  charge  and  the 
other  a  negative  charge  by  attaching  them  to  some 
electro-motive  source,  such  as  a  galvanic  cell,  we  have 
again  our  liquid  condenser,  or  electret.  Since  the  hydro- 
gen atoms  are  positively  charged  and  the  oxygen  atoms 
negatively  charged,  they  will  stretch  themselves  along 
the  strain  lines,  the  oxygen  atoms  towards  the  positive 
electrode,  the  hydrogen  atoms  towards  the  negative  elec- 
trode. Immediately  at  the  surfaces  of  the  electrodes,  the 
molecules  will  be  torn  apart,  and  the  hydrogen  atoms  will 
give  up  their  charges  to  the  negative  electrode,  while  the 
oxygen  atoms  give  up  their  charges  to  the  positive  elec- 
trode. The  procession  of  ions  begins,  and  each  atom  will 
deposit  its  charge  as  if  it  were  a  living  carrier  with  a  bucket- 
ful of  a  certain  definite  quantity  of  electricity.  The 
buckets  of  the  oxygen  carriers  hold  exactly  twice  as  much 
as  those  of  the  hydrogen  carriers,  but  as  there  are  twice 
as  many  of  the  latter  as  of  the  former,  the  total  quantities 
transferred  are  equal  for  both  sides.  Each  carrier  makes 
only  a  single  journey.  When  the  atom  has  deposited  its 
measure  it  is  discharged  and  is  no  longer  subject  to  the 
influence  of  the  field. 

Suppose  we  are  using  the  zinc-copper-acid  cell  for  the 
electro-motive  source.  It  will  seem  as  if  a  current  were 
flowing,  but  actually  there  is  no  flow.  The  two  cells  are 
absolute  nonconductors,  breaking  the  metallic  circuit 
at  two  places.  However,  in  both  cells,  the  carriers  are 
busy  ferrying  over  the  electricity,  we  might  say,  from  one 


MECHANICS  65 

bank  to  the  other.  In  the  galvanic  cell,  the  ferrymen  are 
the  hydrogen  atoms  and  the  S04  radicles,  while  in  the 
water  cell,  the  ferrymen  are  the  H  and  0  atoms.  It  is 
as  if  a  fluid  were  being  pumped  along  in  a  hose,  but  at  two 
places  the  hose  is  broken.  The  only  way  to  overcome  these 
obstacles  is  to  form  two  bucket  lines,  and  at  each  break 
a  line  of  buckets  is  seen  forwarding  the  fluid  with  full 
buckets  in  one  direction  while  a  line  of  empty  buckets  is 
coming  back  in  the  other  direction.  The  number  of 
buckets  used  measures  very  accurately  the  amount  of 
fluid  transferred. 

In  the  water  cell,  we  have  decomposed  the  water  mole- 
cules, and  this  process  of  tearing  apart  molecules  is  called 
electrolysis.  The  oxygen  is  deposited  at  the  positive 
electrode  and  the  hydrogen  at  the  negative  electrode, 
without  any  charges,  whereas  they  previously  had  equal 
and  opposite  charges,  and  by  virtue  of  these  charges  were 
able  to  combine  into  molecules  forming  water.  The 
galvanic  cell  has  done  work,  while  the  water  cell  has  had 
work  done  upon  it.  The  amount  of  current,  or  quantity 
of  ether,  necessary  to  transfer  given  amounts  of  electro- 
lytes is  readily  computed,  and  vice  versa,  the  amount  of 
electrolytes  deposited  gives  us  a  very  accurate  measure  of 
the  amount  of  current  used.  It  is  evident  that  twice  the 
amount  of  current  will  be  necessary  to  deposit  a  given 
amount  of  Hg  from  the  compound  HgCl2)  as  from  the 
compound  HgCl. 

Grotthuss  (in  1805)  framed  a  hypothesis  that  the  mole- 
cules of  an  electrolyte  aligned  themselves  along  the  strain 
lines,  their  positive  and  negative  sides  being  directed 
towards  the  opposite  electrodes.  This  they  undoubtedly 
do.  He  further  supposed  that  under  a  sufficiently  power- 
ful current  in  the  liquid  (at  that  time  it  was  supposed  that 
a  current  could  flow  through  a  liquid)  the  molecules  were 
disrupted  throughout  the  entire  line,  the  positive  half  of 
one  uniting  immediately  with  the  adjacent  negative  half 


66  ELECTRICAL 

of  the  next  one,  and  that  at  the  extreme  ends  only  a  single 
ununited  component  was  left.  Clausius  very  properly 
objected  that  a  very  great  force  must  be  required  to  dis- 
rupt all  the  molecules  simultaneously,  and  that  below  a 
certain  minimum  strength  of  current,  no  decomposition 
could  occur.  Now  the  action  of  even  the  weakest  fields 
can  produce  some  decomposition.  When  the  molecules 
are  facing  promiscuously,  those  next  to  the  electrodes  can 
exert  no  inductive  action  upon  them,  but  if  a  field  is 
sufficient  to  polarize  at  least  some  of  them,  then  the  in- 
ductive action  of  those  molecules  directed  towards  the 
surface  acting  jointly,  is  appreciable,  and  decomposition 
results.  The  actual  disruption  of  the  molecules  takes 
place  only  directly  at  the  surfaces  of  the  electrodes,  and 
not  in  other  parts  of  the  line. 

According  to  the  modern  theory,  the  molecules  of  a 
compound  in  solution  are  always  more  or  less  dissociated, 
their  ions  continually  separating  and  recombining.  The 
theory  further  assumes  that  electrolysis  is  carried  on  solely 
by  such  dissociated  ions,  and  that  if  no  dissociated  ions 
were  originally  present,  electrolysis  would  be  impossible. 
But  electrolysis  can  be  carried  on  equally  well  with  or 
without  free  ions  in  the  original  solution.  Even  if  free 
ions  should  be  present  previously  to  applying  the  electric 
field,  they  will  carry  on  only  a  part  of  the  process,  for  there 
must  also  be  a  disruption  by  induction  of  the  extreme 
molecules  next  to  the  electrodes.  Since  in  framing  any 
explanation  it  is  wise  to  postulate  no  more  conditions  than 
are  absolutely  necessary,  and  since  the  assumption  of 
previously  existing  free  ions  is  unnecessary  for  the  explana- 
tion of  electrolysis,  we  shall  not  consider  it  in  the  present 
discussion.  Whether  under  other  circumstances  and  in 
connection  with  other  phenomena,  it  is  necessary  to  as- 
sume such  dissociation  as  a  general  condition  of  all  solu- 
tions, is  a  question  which  does  not  concern  us  here.  It 
may  be  remarked  that  the  theory  was  originally  pro- 


MECHANICS 


67 


pounded  because  it  was  thought  that  electrolysis  could  be 
explained  in  no  other  way. 

In  Fig.  7,  we  have  a  diagrammatic  representation  of  the 
condition  of  the  charges  in  a  water  molecule  when  (1)  in 


H 


o 


<£) 


H 


Fig.7 


the  interior  of  the  liquid,  and  when  (2)  close  to  the  surface 
of  an  electrode.  In  the  former  position  the  charges 
mutually  attract  each  other  towards  the  centre  of  the 
molecule.  In  the  latter  position,  the  charge  on  the  oxygen 
atom  is  attracted  by  the  positive  charge  on  the  electrode, 
while  the  hydrogen  charges  are  repelled,  and  released 
from  their  former  strain  they  assume  a  more  normal 
condition — spherical.  It  is  evident  that  the  attraction 
of  the  electrode  on  the  oxygen  charge  is  greater  than  the 
resultant  in  this  direction  of  the  attractions  of  the  hydro- 
gen charges.  Hence  the  molecule  must  be  disrupted. 


MAXWELL'S  THEORY 


The  name  and  work  of  Maxwell  have  exercised  such  a 
great  influence  in  the  domain  of  electricity  that  it  would 
seem  proper,  in  such  a  book  as  this,  to  touch  briefly  upon 
a  few  main  points  of  his  theory.  Some  idea  of  his  "Elec- 
tricity and  Magnetism"  may  be  formed  from  the  com- 
ments of  various  writers.  One  describes  it  as  "Pretty 
stiff  reading."  Another  says,  "To  ask  a  student  to  at- 
tempt to  assimilate  the  contents  of  the  two  volumes  of 
Maxwell  in  a  year,  or  even  in  two  years,  is  only  to  expose 
him  to  the  severest  pangs  of  mental  indigestion.  Again 
Maxwell's  own  views  are  there  presented  by  him  with  not 
the  greatest  clearness,  while  severe  demands  are  made 
upon  the  student's  mathematical  attainments."  Lodge 
says  of  it,  "Much  of  it  is  rough  hewn.  It  contains  nu- 
merous misprints  and  errata,  and  part  of  the  second 
volume  is  so  difficult  as  to  be  almost  unintelligible.  Some, 
in  fact,  consists  of  notes  written  for  private  use,  and  not 
prepared  for  publication."  The  fact  is  that  some  parts  of 
Maxwell's  book  cannot  be  understood  simply  because 
they  are  not  understandable,  and  some  other  parts  because 
they  are  not  so.  Thus,  while  the  advice,  often  lightly 
given,  to  "Read  Maxwell,"  can  hardly  be  recommended  as 
affording,  even  to  a  mathematician,  a  profitable  return  for 
the  time  spent,  still  it  is  advisable  that  the  student  of  elec- 
tricity should  have  some  knowledge  of  Maxwell's  theory, 
if  it  can  be  considered  a  theory.  For  Herz  said,  "Max- 
well's theory  is  simply  Maxwell's  system  of  equations." 

Nevertheless,  we  owe  to  this  great  man  the  beginnings 
of  the  enormous  advances  both  theoretically  and  in 

68 


MECHANICS  69 

practical  applications  which  have  transformed  our  civil- 
ization in  a  generation.  Faraday  had  spent  his  life  in 
emphasizing  the  fact  that  the  acting  body  was  not  the 
only  thing  deserving  of  attention,  but  that  very  important 
things  were  also  happening  in  the  immediate  neighborhood 
of  an  electrified  or  magnetized  body.  Whence,  as  was  in- 
evitable, a  number  of  later  writers  have  proclaimed  that 
the  dielectric  played  the  chief  role  in  all  actions,  that  of 
the  acting  body  being  insignificant.  But  Faraday  never 
said  that,  for  after  all  the  originating  source  is  "the  thing," 
although  not  the  only  thing,  as  had  been  thought  before. 

Maxwell  did  not  discover  the  ether,  but  he  rediscovered 
it.  He  called  the  attention  of  mankind  to  this  greatest 
part  of  the  universe,  of  which  they  had  previously  been 
sublimely  unconscious,  and,  compared  with  which,  the 
mass  and  energy  of  gross  matter  is  infinitesimal.  Only 
one  hundred  years  before  Maxwell,  the  world  had  known 
little  more  of  electricity  than  Aristotle  did.  In  his  time 
old  habits  of  thinking  persisted.  The  idea  of  action  at  a 
distance  without  an  intervening  medium  was  general, 
although  Newton  had  clearly  recognized  the  necessity  of 
such  a  medium.  Maxwell  shook  himself  free  of  all  the 
old  fetters,  and  building  where  Faraday  left  off,  discovered 
that  all  electrical  actions  were  carried  by  the  ether. 
He  also  found  that  light  waves  instead  of  being  the  vi- 
brations pictured  in  the  old  undulatory  theory,  were  of 
a  totally  different  character,  and  although  he  failed  to  rec- 
ognize clearly  and  exactly  what  that  character  was,  yet 
he  showed  that  they  were  electro-magnetic  phenomena. 
These  two  things  may  be  summed  up  as  his  chief  achieve- 
ments— and  they  are  enough. 

We  shall  now  mention  briefly  some  of  the  chief  points 
of  his  theory  in  detached  statements.  *"One  can  imagine 
that  the  electro-magnetic  strain  condition  arises  through  a 

*Kalahne.  Neuere  Forschungen  auf  dem  Gebiet  der  Electrizitat 
und  ihre  Anwendungen. 


70  ELECTRICAL 

change  in  the  dielectric,  which  corresponds  to  a  distortion 
of  the  particles  in  an  elastic  body.  Maxwell,  following 
Faraday,  describes  this  change  in  the  dielectric  as  a 
dielectric  displacement,  though  this  need  not  necessarily 
imply  an  actual  displacement  of  the  ether  particles." 
This  is  quoted  to  show  the  vagueness  of  some  of  his  ideas. 
Actually,  there  must  be  some  displacement  (motion)  of 
the  ether  particles.  Maxwell's  idea  seems  to  be  rather 
that  of  a  strain  moving  progressively  through  the  medium 
— an  abstract  condition — while  the  medium  itself  remains 
at  rest. 

In  every  part  of  a  dielectric  both  kinds  of  electricity 
(positive  and  negative)  are  supposed  to  be  present  in  a 
neutral  condition.  In  the  phenomenon  of  induction,  both 
these  electricities  previously  exist  in  unlimited  quantities 
in  the  conductor,  and  their  separation  results  from  a 
stationary  condition  of  strain  set  up  in  the  medium.  We 
have  seen  that  the  induced  charges  are  applied  to  the 
conductor  by  the  waves  radiating  from  the  inducing  body, 
and  they  are  held  apart  by  the  wave  force.  According  to 
Maxwell  these  two  kinds  of  electricity,  which  are  present 
everywhere,  are  not  only  separated  in  conductors,  but  also 
in  all  dielectrics  by  a  condition  of  strain.  The  separation 
in  dielectrics,  however,  is  only  through  infinitesimal  dis- 
tances, and  what  he  calls  the  dielectric  displacements 
consists  of  such  separations  of  the  two  electricities.  The 
condition  of  strain  which  causes  these  displacements,  and 
the  displacements  themselves,  or  the  cause  and  effect, 
are  treated  as  mathematically  equivalent.  It  is  as  if  a 
lot  of  little  balls  were  imbedded  in  the  medium  and  had 
their  neutral  electricity  separated  into  its  two  components. 
The  displacement  takes  place  successively  along  such  a 
row  of  balls  in  a  line  of  force,  by  influence.  Here  we  have 
a  curious  reversion  to  the  old  idea  of  action  at  a  distance. 
It  seems  as  if  the  idea  of  action  through  a  finite  distance 
is  repugnant,  but  this  is  obviated  by  strewing  a  lot  of 


MECHANICS  71 

minute  balls  throughout  space,  as,  in  that  case,  the  action 
will  be  only  over  infinitesimal  distances.  But  to  this 
statement,  Kalahne  hastens  to  add  that  it  should  rather 
be  taken  as  a  figurative  presentation  of  the  case,  which 
need  not  necessarily  be  actually  so.  Whenever  we  imag- 
ine that  we  have  some  material  platform  to  stand  upon, 
it  is  immediately  torn  down  from  under  us.  In  a  certain 
sense,  Maxwell  was  right  in  supposing  that  the  two  kinds 
of  electricity  exist  everywhere  in  a  neutral  state,  for  the 
neutral  ether  becomes  positive  or  negative  electricity 
according  as  it  is  condensed  or  rarefied.  But  Maxwell 
did  not  understand  it  in  this  sense,  since  to  him  the  ether 
was  incompressible. 

Lines  of  electric  force  are  merely  mathematical  repre- 
sentations of  observed  phenomena,  independent  of  any 
special  suppositions  as  to  the  nature  of  the  dielectric  dis- 
placement. In  a  condenser  which  is  charged  by  a  current 
source,  while  the  charge  on  the  plates  is  increasing  and  the 
current  is  flowing,  the  lines  of  force  in  the  dielectric  in- 
crease. Maxwell  considered  the  increase  of  the  lines  of 
force,  or  what  is  equivalent,  the  dielectric  displacement 
currents,  could  be  regarded  as  a  direct  continuation  of  the 
current.  There  was  thus,  wherever  a  current  was  flowing, 
no  such  thing  as  an  open  circuit.  All  circuits  were  closed 
circuits,  and  every  part  of  a  circuit  had  its  current  with 
its  accompanying  magnetic  field.  In  the  conducting  part 
there  was  an  ordinary  current,  while  in  the  dielectric 
there  was  a  displacement  current.  If  we  are  content  to 
deal  with  metaphysical  abstractions,  we  may  accept  this 
view,  but  if  we  have  strict  regard  for  the  actual  facts,  it  is 
not  so.  We  have  seen  that  the  waves  traversing  the  field 
in  a  dielectric,  consist  of  alternating  currents  in  the  direc- 
tion of  the  lines  of  force.  These,  in  a  certain  sense,  may  be 
considered  displacement  currents,  but  they  are  not  Max- 
well's displacement  currents,  which  flowed  only  one  way. 

The  ether  is  a  dielectric,  and  Maxwell  considered  that 


72  ELECTRICAL 

displacement  currents  occur  in  the  ether,  as  in  all  di- 
electrics. He  thought  that  each  displacement  current 
should  have  its  own  magnetic  field,  just  as  current  in  a 
conductor  is  surrounded  by  a  magnetic  field.  As  a  matter 
of  fact  currents  in  the  free  ether,  such  as  the  to  and  fro 
currents  of  a  longitudinal  wave,  or  the  hypothetical  dis- 
placement currents  of  Maxwell,  do  not  have  any  magnetic 
field.  The  magnetic  field  accompanying  a  current  in  a 
conductor  is  formed  by  the  resistance  opposed  to  the 
current  by  the  atomic  surfaces. 

Assuming  displacement  currents  in  the  ether  and  that 
they  are  accompanied  by  magnetic  fields,  it  is  possible 
to  form  equations  which  express  the  time  relation  of  the 
variations  of  the  electric  force  (which  we  can  consider  in- 
differently a  line  of  electric  force  or  a  displacement  current) 
to  its  magnetic  field,  or  to  the  space  distribution  of  the 
magnetic  strain  condition.  This  gives  us  one  set  of  Max- 
well's equations  for  electro-magnetic  disturbances  in  space. 

Then  he  considered  that  the  variation  of  the  magnetic 
force  should  likewise  cause  variations  in  the  electric  field, 
or  displacement  currents.  The  next  step  was  to  suppose 
that  the  magnetic  forces  and  the  electric  forces  possessed, 
what  are  known  in  mathematics,  as  conjugate  properties. 
That  is,  the  expressions  for  the  variations  of  the  one 
quantity  in  terms  of  the  other,  can  conversely  give  the 
variations  of  the  other  in  terms  of  the  first,  by  simply 
interchanging  the  symbols  of  the  one  for  the  other. 

There  was  now  a  difficulty.  One  set  of  equations — 
those  for  the  electric  forces — had  an  expression  for  a 
displacement  current.  There  could  be  no  such  thing  as 
a  magnetic  displacement  current,  or  a  magnetic  current 
of  any  kind.  So  the  corresponding  expression  was  simply 
left  out.  Thus  Maxwell's  two  sets  of  equations  were 
derived — one  set  for  the  electrical  forces,  the  other  set 
for  the  magnetic  forces. 

The  mechanism  by  which  the  propagation  of  these 


MECHANICS  73 

electro-magnetic  waves  is  accomplished  is  left  "in  the  air." 
There  are  not  necessarily  any  actual  physical  vibrations, 
or  any  motion  even,  although  their  possibility  is  not  nec- 
essarily excluded.  The  process  is  simply  a  periodic  and 
progressive  rise  and  fall  of  electric  and  magnetic  forces 
from  point  to  point  in  space.  Certain  hypothetical  forces, 
which  are  pure  abstractions,  are  dealt  with  in  certain 
equations,  and  a  result  is  obtained.  It  is  shown  that  both 
the  magnetic  and  electric  forces  lie  in  the  plane  of  the  wave 
and  are  perpendicular  to  each  other.  Of  course  electric 
and  magnetic  forces,  mutually  interdependent,  must  be 
perpendicular  to  each  other. 

If  we  should  begin  to  make  some  mental  image  as  to 
the  nature  of  these  disturbances,  we  should  be  told  that 
we  must  not  think  of  anything  tangible,  not  even  of 
motion,  but  merely  of  a  passing  rise  and  fall  of  energy  at 
some  point,  and  that  the  electric  and  magnetic  forces  were 
perpendicular  to  each  other. 

Now  we  have  seen  that  an  electro-magnetic  wave  con- 
sists of  a  spreading  out  of  vortex  tubes.  The  electric 
force,  or  the  current  sheet,  which  corresponds  to  what 
Maxwell  calls  the  displacement  current,  is  circular  and 
has  all  directions.  One  of  these  directions  is,  of  course, 
in  the  plane  of  the  wave,  and  the  direction  of  the  magnetic 
force,  or  axis  of  the  tube,  is  in  the  plane  of  the  wave.  Now 
it  happens  that  the  only  motion  of  the  current  sheet  which 
can  possibly  be  detected  by  the  eye,  or  in  any  other  way, 
is  the  one  in  the  plane  of  the  wave,  since  the  effects  of  the 
motions  in  all  other  directions  are  self-eliminatory.  This 
motion  and  the  magnetic  line  lie  in  the  plane  of  the  wave, 
and  they  are  perpendicular  to  each  other.  So  far  we  have 
a  corroboration  of  Maxwell's  theory  as  to  the  position  and 
direction  of  the  forces.  It  follows  that  a  vortex  tube  is  a 
practical  realization  of  Maxwell's  abstract  reasoning,  as 
far  as  that  is  possible,  and  it  is  fairly  evident  that  there 
can  be  no  other  motion  which  is  such  a  realization. 


MISCELLANEOUS 


We  have  hitherto  stood  upon  tolerably  firm  ground. 
We  can  assume  with  a  fair  degree  of  confidence  that  the 
ether  and  electricity  are  synonomous.  A  positive  charge 
of  electricity  is  a  condensed  mass  of  ether.  A  negative 
charge  of  electricity  is  a  rarefied  portion  of  ether.  At- 
traction and  repulsion  generally  are  due  to  longitudinal 
waves,  the  action  depending  upon  the  kind  of  the  wave 
(there  being  two  kinds),  and  upon  whether  the  body  is 
denser  or  less  dense  than  the  medium.  This  action  is 
not  confined  to  the  ether,  but  is  seen  in  all  media.  Thus 
two  tuning  forks  emitting  longitudinal  waves  attract  each 
other.  A  tuning  fork  attracts  a  balloon  filled  with  car- 
bonic dioxide,  while  it  repels  one  filled  with  hydrogen. 
The  radiations  from  the  surface  of  a  carbonic  dioxide 
balloon  repel  a  similar  balloon,  while  attracting  a  hydrogen 
balloon.  A  hydrogen  balloon  repels  a  similar  balloon  while 
attracting  a  positive  balloon.  Gross  matter  and  negative 
charges  of  electricity  radiate  positive  waves;  positive 
charges  of  electricity  radiate  negative  waves.  Magnetic 
lines  are  linear  vortices  in  the  ether,  and  electro-magnetic 
waves  consist  of  trains  of  such  vortices  travelling  outward 
with  the  normal  velocity  of  the  medium.  Chemical 
affinity  is  the  attraction  of  equal  and  opposite  charges  on 
the  atoms  or  radicles  of  a  molecule. 

There  are,  however,  many  phenomena  outstanding 
which  must  continue  to  be  the  subject  of  speculation. 
That  light  rays  should  continue  in  a  straight  line,  as  sound 
waves  do  not,  is  easily  intelligible  from  their  vortex 
structure.  The  great  difficulty  with  the  old  undulatory 

74 


MECHANICS  75 

theory  was  how  to  account  for  polarized  rays.  Knowing 
that  such  rays  consist  of  trains  of  vortex  tubes,  the  diffi- 
culty is  reversed,  and  it  might  seem  that  all  rays  should 
be  polarized.  It  is  evident,  however,  that  the  promiscu- 
ous positions  of  these  tubes  in  ordinary  light  is  because 
the  vibrations  are  continually  shifting  in  direction.  That 
they  should  be  deflected  slightly  from  a  straight  course 
on  grazing  a  sharp  edge,  we  should  expect,  since  the 
grazing  side  of  a  vortex  will  be  slightly  retarded  or  acceler- 
ated according  to  the  direction  of  its  rotation,  with  the 
result  that  the  vortex  will  be  deflected  above  or  below  the 
edge.  That  the  diffraction  bands  should  be  wider  and 
extend  to  a  greater  distance  above  the  edge  than  below, 
we  likewise  could  have  predicted. 

We  have  seen  that  the  rate  of  the  outflow  of  energy  from 
a  body  at  a  higher  potential  than  its  surroundings  is 
proportional  to  the  excess  of  its  potential,  when  the  energy 
streams  out  in  the  form  of  longitudinal  waves.  This  is 
not  the  case  when  the  energy  is  radiated  in  the  form  of 
electro-magnetic  waves.  The  number  of  vortices  gener- 
ated in  a  conductor  in  a  given  time  is  proportional  to  the 
current  and  also  to  the  suddenness  with  which  the  current 

i 

rises,  or  it  is  proportional  to  J  £_•    Hence  the  number 

o        dt 

of  vortices  generated  in  unit  time  should  be  proportional 
to  the  square  of  the  current.  Now  the  magnetic  energy 
in  a  vortex  we  have  seen  to  be  measured  by  the  square  of 
the  velocity  of  the  current  sheet.  This  current  sheet  has 
the  same  velocity  as  the  generating  current  at  the  instant 
that  it  leaves  the  wire,  and  a  current  is  measured  by  its 
velocity.  Hence  the  total  output  of  energy  in  unit  time 
should  be  proportional  to  the  fourth  power  of  the  current, 
and  since  the  current  is  proportional  to  the  pressure,  it 
should  also  be  proportional  to  the  fourth  power  of  the 
potential.  Stefan's  formula  states  that  the  electro-mag- 


76  ELECTRICAL 

netic  radiation  (heat)  of  the  sun  is  proportional  to  the 
fourth  power  of  its  temperature  or  potential.  Since  the 
surroundings  of  the  sun  into  which  this  radiation  takes 
place  are  at  the  absolute  zero,  or  the  temperature  of 
space,  the  potential  must  be  measured  from  the  absolute 

77 

zero.     Stefan's  formula  is  —  =  r4,  or  the  amount  of  heat 

t 

radiated  per  unit  surface  of  the  sun  per  unit  time  is 
measured  by  the  fourth  power  of  its  absolute  surface 
temperature.  It  is  more  than  a  formula  and  can  be  con- 
sidered as  expressing  a  law.  The  amount  of  energy 
radiated  by  a  wire,  in  wireless  telegraphy,  in  unit  time, 
should  be  proportional  to  the  fourth  power  of  the  average 
pressure  in  the  wire.  This  law  has  not  as  yet  been  ex- 
amined in  connection  with  radio-telegraphy,  but  it  would 
doubtless  find  confirmation. 

When  an  atom  vibrates,  or  moves  to  and  fro  along  a 
line,  it  generates  both  electro-magnetic  waves  and  longi- 
tudinal waves.  The  edges  of  the  condensed  ether  in  front 
curl  round  over  the  rarefied  ether  behind  and  thus  a  vortex 
is  formed,  while  from  the  central  part  the  longitudinal 
wave  is  started.  Thus,  with  every  excursion  in  one 
direction  the  compressed  half  of  a  longitudinal  wave  is 
formed  as  well  as  a  vortex  rotating  in  a  definite  direction, 
while,  with  the  return  excursion,  the  expanded  half  of 
the  longitudinal  wave  is  completed  and  another  vortex 
rotating  in  the  opposite  direction  is  formed.  The  direction 
of  the  alternating  currents  in  the  longitudinal  wave  is  the 
direction  of  the  vibratory  motion,  while  the  vortex  rings 
spread  out  in  a  plane  perpendicular  to  this  direction. 
The  electric  forces  (the  currents)  are  perpendicular  to  the 
magnetic  forces  (the  vortex  filaments),  as  is  inevitable. 
The  two  kinds  of  energy  radiated  are  not  equal,  for  while 
we  may  suppose  the  longitudinal  wave  energy  to  remain 
measurably  constant,  the  electro-magnetic  energy  radiated 


MECHANICS  77 

increases  as  the  fourth  power  of  the  pressure,  and  this 
varies  as  the  frequency  of  the  vibrations.  Hence  it  would 
seem  probable  that  the  attraction  exerted  by  a  body  is  not 
influenced  by  its  temperature,  while  the  electro-magnetic 
radiation  varies  as  the  fourth  power  of  the  temperature. 

If  we  seal  electrodes  into  a  bulb  from  which  a  gas  has 
been  partially  exhausted,  we  can  transfer  electricity 
through  it.  The  transference  is  by  convection,  as  in  the 
case  of  an  electrolyte.  The  molecules  of  the  gas  receive 
charges  and  are  violently  repelled.  They  become  dis- 
sociated into  their  atoms,  either  from  the  charges  they 
receive  or  from  the  violent  impacts  on  the  electrodes. 
When  the  source  of  energy  is,  as  usual,  an  inductorium, 
the  field  is  very  strong  and  practically  constant,  the  lines 
of  force  extending  from  the  anode  to  the  cathode. 

Certain  bodies  called  electrons  are  produced,  the  nature 
of  which  is  not  yet  fully  determined.  They  are  certainly 
not  atoms  of  electricity,  for  electricity  is  the  ether,  and  the 
ether  as  far  as  we  know  is  a  continuum.  If  they  were 
ether  atoms,  they  would  not  be  differentiated  from  the 
rest  of  the  ether,  and  therefore  could  not  be  observed. 
They  may  possibly  be  minute  vortex  rings — rings  without 
any  central  lumen — which  are  given  off  from  the  elec- 
trodes as  the  current  surges  violently  and  brings  up  with 
an  impact  on  the  end  surfaces.  We  have  seen  that  a 
rising  current  in  a  wire  is  full  of  such  vortices  which  are 
shoved  outward  around  the  wire.  From  an  end  surface 
they  may  be  simply  projected  away  normally  to  the 
surface. 

Such  vortices  are  very  much  less  dense  than  the  ether. 
Consequently  they  constitute  a  negative  charge,  and 
may  be  considered  to  be  mainly  a  negative  charge  with 
practically  no  mass.  In  an  electric  field  they  are  urged 
towards  the  positive  electrode  with  the  standard  velocity ; 
in  a  magnetic  field  with  its  lines  perpendicular  to  their 
line  of  flight,  they  are  deflected  in  the  same  direction  as  a 


78  ELECTRICAL 

wire  would  be  carrying  a  current  from  the  anode  to  the 
cathode.  They  should  traverse  the  space  from  the 
cathode  to  the  anode  with  the  standard  velocity,  and  with 
proper  conditions  they  very  nearly  attain  this  velocity. 
Where  there  are  too  many  atoms  and  molecules  of  the  gas 
in  their  path,  their  progress  is  impeded,  and  their  velocity 
may  fall  to  two-thirds  of  the  standard  velocity,  or  even 
lower. 

When  electrons  strike  upon  a  resisting  surface  they  give 
rise  to  what  are  known  as  X  rays.  It  is  possible  that 
they  are  burst  by  the  violent  impact  and  cease  holding 
their  vacua.  They  thus  become  dissipated  into  the  gen- 
eral ether  and  cease  being  a  differentiated  part  of  it.  Their 
energy,  which  is  magnetic,  becomes  transformed  into  a 
violent  explosive  ether  wave,  just  as  when  a  vacuum 
bulb  is  dashed  against  an  object  an  explosive  air  wave 
results.  As  in  air  such  a  violent  single  unidirectional 
wave  may  travel  with  many  times  the  standard  velocity, 
so  these  explosive  waves,  or  X  rays,  may  move  with  a 
velocity  which  is  limited  only  by  the  energy  expended  and 
the  suddenness  with  which  it  is  expended.  But  we  are 
here  in  the  realm  of  speculation. 


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4r* 


NOV  11  19«M 


290ct'55LT 


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